Society for Industrial and Applied Mathematics: SIAM Journal on Applied Mathematics: Table of Contents

Reconstruction of the Heat Relaxation Index in the Phonon Transport Equation

Peiyi Chen — 2026-05-04T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 751-775, June 2026.
Abstract. For nanomaterials, the concept of heat conductivity needs to be revisited. At this fine scale, heat is propagated using the phonon transport equation, an ab initio model derived from first principles. In this problem, a material’s thermal property is coded in a coefficient termed the relaxation time [math], depending on the phonon frequency. We propose a novel inverse problem in this paper that infers the relaxation time using a material’s temperature response upon heat injection. This inverse problem is formulated in a PDE-constrained optimization and is numerically solved by the stochastic gradient descent method (SGD) and its variants. In the execution of SGD, the Fréchet derivative is computed and Lipschitz continuity is proved. This approach, in comparison to the earlier studies, enhances the ab initio concept of heat conduction in nanostructures associated to nanomaterials.

Dynamic One-Photon Localization in a Discrete Model of Quantum Optics

Joseph Kraisler — 2026-05-04T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 776-790, June 2026.
Abstract. We consider a recently proposed model for the propagation of one-photon states in a random medium of two-level atoms. We demonstrate the existence of Anderson localization of single-photon states in an energy band centered at the resonant energy of the atoms. Additionally, for a bosonic model of the atoms the results can be extended to multi-photon states.

Inheritance of Intracellular Viral RNA in a Multiscale Model of Hepatitis C Infection

Tyler Cassidy — 2026-05-04T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 791-813, June 2026.
Abstract. Multiscale mathematical models of hepatitis C infection have been instrumental in our understanding of direct acting antivirals. These models include the mechanisms driving intracellular viral production and explicitly model the intracellular concentration of viral RNA. However, incorporating proliferation of infected hepatocytes in these models can be subtle, as infected daughter cells inherit viral RNA from the proliferating mother cell. Here, we show how to incorporate this inheritance within a multiscale model of HCV infection. As in typical multiscale models of HCV infection, we show that this model is mathematically equivalent to a system of ordinary differential equations and perform bifurcation analysis of the resulting ODE demonstrating that proliferation of infected hepatocytes can lead to infection persistence, even if the basic reproduction number is less than 1.

Forecasting Public Sentiments via Mean Field Games

Michael V. Klibanov — 2026-05-05T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 814-838, June 2026.
Abstract. Motivated by the goal of forecasting public sentiments, we consider a forecasting problem in the context of the mean field games theory. We develop a numerical method, which is a version of the so-called convexification method. We provide theoretical convergence analysis that establishes global convergence of the method with a convergence rate. We also conduct numerical experiments that demonstrate the accurate performance of the convexification technique and highlight some promising features of this approach.

On Nonlinear Closures for Moment Equations Based on Orthogonal Polynomials

Eda Yilmaz — 2026-05-06T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 839-869, June 2026.
Abstract. In the present work, an approach to the moment closure problem on the basis of orthogonal polynomials derived from Gram matrices is proposed which is inspired by [R. O. Fox and F. Laurent, SIAM J. Appl. Math., 82 (2022), pp. 750–771]. The new theory comes with an explicit formulation of the closure relation and satisfies a generalized gauge theory in consistency with affine transformations of the phase space. It also allows us to explicitly prove global hyperbolicity of the resulting moment equations for an arbitrary number of moments. Numerical studies are carried out on local distributions to investigate different variants of the new closures in comparison to other moment closure methods, such as Grad’s closure and the maximum-entropy method. The proposed “Gramian” closure is shown to be able to provide very accurate predictions of the next higher moment for a wide range of distribution functions.

A Unified Variational Model for Grain Boundary Dynamics Incorporating Microscopic Structure

Luchan Zhang — 2026-05-08T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 870-897, June 2026.
Abstract. Recent experiments, atomistic simulations, and theoretical predictions have identified various new types of grain boundary motions that are controlled by the dynamics of underlying microstructure of line defects (dislocations or disconnections), to which the classical motion by mean curvature model does not apply. Different continuum models have been developed by upscaling from discrete line defect dynamics models under different settings (dislocations or disconnections, low angle grain boundaries or high angle grain boundaries, etc.) to account for the specific detailed natures of the microscopic dynamics mechanisms, and these continuum models are not in the variational form. In this paper, we propose a unified variational framework to account for all the underlying line defect mechanisms for the dynamics of both low and high angle grain boundaries and the associated grain rotations. The variational formulation is based on the developed constraints of the dynamic Frank–Bilby equation that governs the microscopic line defect structures. The proposed variational framework is able to recover the available models for different motions under different conditions. The unified variational framework is more efficient for describing the collective behaviors of grain boundary networks at larger length scales. It also provides a mathematically tractable basis for rigorous analysis of these partial differential equation models and for the development of efficient numerical methods.

Pointwise Distance Distributions for Detecting Near-Duplicates in Large Materials Databases

Daniel E. Widdowson — 2026-05-08T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 898-918, June 2026.
Abstract. Many real objects are modeled as discrete sets of points, such as corners or other salient features. For our main applications in chemistry, points represent atomic centers in a molecule or a solid material. We study the problem of classifying discrete (finite and periodic) sets of unordered points under isometry, which is any transformation preserving distances in a metric space. Experimental noise motivates the new practical requirement to make such invariants Lipschitz continuous so that perturbing every point in its [math]-neighborhood changes the invariant up to a constant multiple of [math] in a suitable distance satisfying all metric axioms. Since the given points are unordered, the key challenge is to compute all invariants and metrics in a near-linear time of the input size. We define the Pointwise Distance Distribution (PDD) for any discrete set and prove, in addition to the properties above, the completeness of PDD for all periodic sets in general position. The PDD can compare nearly 2 million crystals from the world’s five largest databases within 2 hours on a modest desktop computer. The impact is upholding data integrity in crystallography because the PDD will not allow anyone to claim a “new” material as a noisy disguise of a known crystal.

Analyzing the Nematic Liquid Crystal Droplet with an Improved Diffuse-Interface Landau–de Gennes Model

Baoming Shi — 2026-05-08T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 919-944, June 2026.
Abstract. The nematic liquid crystal droplet problem is of significant interest due to the complex interplay between variable droplet shapes and orientation fields, with numerous applications in physics and material science. Here we introduce an improved diffuse-interface Landau–de Gennes model for nematic liquid crystal droplets, which eliminates an artificial penalty term from [Wu et al., SIAM J. Math. Anal., 57 (2025), pp. 4358–4395] that is inconsistent with the classical droplet problem. We prove the existence of minimizers and [math]-convergence to a physically interpretable sharp-interface energy functional. We also present asymptotic solutions across the interface between the interior nematic droplet and external isotropic phase. Numerical simulations reveal optimal droplet configurations—radial, ring, and tactoid—highlighting the mutual influence between topological defects and droplet morphology. Furthermore, we construct a phase diagram of (meta)stable configurations as a function of temperature and domain size, delineating distinct stability regimes for biaxial and uniaxial phases.

Mean-Field Analysis of a Random Asset Exchange Model with Probabilistic Cheaters

Fei Cao — 2026-05-22T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 945-960, June 2026.
Abstract. We investigate a variant of the standard Bennati–Dragulescu–Yakovenko game [A. Dragulescu and V. M. Yakovenko, Eur. Phys. J. B, 17 (2000), pp. 723–729] inspired by the very recent work [K. Blom, D. E. Makarov, and A. Godec, Phys. Rev. Res., 7 (2024), 013279], where agents involved in a money exchange dynamics are classified into two distinct types called probabilistic cheaters and honest players, respectively. A probabilistic cheater has a positive probability of declaring to have no money to give to other agents in the system, resulting in potential financial benefits from being dishonest about his/her financial status. We provide a mean-field description of the agent-based model (in terms of a coupled infinite-dimensional system of nonlinear ODEs) in the large population limit where the number of players is sent to infinity, and we prove convergence of the coupled mean-field system to its stationary distribution (provided by a mixture of geometric distributions). In particular, the model gives rise to a novel formulation involving a mixture of probability distributions, thereby motivating the introduction of an unusual (generalized) entropy functional tailored to the associated mean-field system.

Averaged Steklov Eigenvalues, Inside-Outside Duality and Application to Inverse Scattering

Lorenzo Audibert — 2026-05-27T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 961-984, June 2026.
Abstract. We introduce a new family of artificial backgrounds corresponding to averaged impedance boundary conditions formulated in an abstract framework. These backgrounds are used to define a finite number of averaged Steklov eigenvalues, which are associated with inverse scattering problems from inhomogeneous media. We prove that these special eigenvalues can be determined from full-aperture, fixed-frequency far fields using the inside-outside duality method. We then numerically demonstrate how this method can be used to reconstruct averaged values of the refractive index.

Regularized Dynamic Optimal Transport for Spatial-Temporal Image Generation

Chen Li — 2026-05-28T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 985-1007, June 2026.
Abstract. Optimal transport (OT) theory and models have been widely applied in the fields of computer vision, machine learning, and image analysis. Among three typical OT model formulations—the Monge, Kantorovich, and dynamical ones—the Kantorovich formulation with entropic regularization is most commonly used in practice due to its simple computational scheme. The other two formulations are rarely regularized since adding regularization terms brings additional difficulties to their theoretical analysis and numerical algorithms. In this paper, we propose a regularized OT model based on the dynamic formulation. We incorporate a [math] regularization term on the momentum field to promote smoothness, and a total variation regularization term on the density field to enhance robustness to noise. We establish the existence and uniqueness of solutions to the regularized dynamic OT model and provide a theoretical analysis based on [math]-convergence. Moreover, we develop a primal-dual algorithm to efficiently solve the resulting optimization problem. Numerical experiments on spatial-temporal image generation tasks demonstrate the effectiveness of the proposed model and the stability and efficiency of the proposed numerical algorithm. The proposed regularized dynamical OT model provides a flexible and theoretically grounded framework for image generation tasks in imaging science.

A Hyperbolic Inverse Problem for Lower Order Terms on a Closed Manifold with Disjoint Data

Matti Lassas — 2026-05-28T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 3, Page 1008-1034, June 2026.
Abstract. We study the unique recovery of time-independent lower order terms appearing in the symmetric first order perturbation of the Riemannian wave equation by sending and measuring waves in disjoint open sets of an a priori known closed Riemannian manifold. In particular, we show that if the set where we capture the waves satisfies a geometric control condition as well as a certain local symmetry condition for the distance functions, then the aforementioned measurement is sufficient to recover the lower order terms up to the natural gauge. For instance, our result holds if the complement of the receiver set is contained in a simple Riemannian manifold.

Neural Fields and Noise-Induced Patterns in Neurons on Large Disordered Networks

Daniele Avitabile — 2026-03-02T08:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 427-456, April 2026.
Abstract. We study pattern formation in a class of high-dimensional neural networks posed on random graphs and subject to spatiotemporal stochastic forcing. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a rigorous mean-field limit, resembling a Wilson–Cowan neural-field equation. The state variables of the limiting systems are the mean and variance of neuronal activity. We select networks whose mean-field equations are tractable and we perform a bifurcation analysis using as a control parameter the diffusivity strength of the afferent white noise on each neuron. We find conditions for Turing-like bifurcations in a system where the cortex is modelled as a ring, and we produce numerical evidence of noise-induced spiral waves in models with a two-dimensional cortex. We provide numerical evidence that solutions of the finite-size network converge weakly to solutions of the mean-field model. Finally, we prove a large deviation principle, which provides a means of assessing the likelihood of deviations from the mean-field equations induced by finite-size effects.

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

Zheng Tan — 2026-03-02T08:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 457-481, April 2026.
Abstract. We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number [math] as [math]. Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

Shape Taylor Expansion for Wave Scattering Problems

Gang Bao — 2026-03-03T08:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 482-505, April 2026.
Abstract. The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high order shape derivatives required for this expansion poses significant challenges with conventional methods. This paper addresses these difficulties by introducing elegant recurrence formulas for computing high order shape derivatives. The derivation employs tools from exterior differential forms, Lie derivatives, and material derivatives. This work establishes a unified framework for computing the high order shape perturbations in scattering problems. In particular, the recurrence formulas are applicable to both acoustic and electromagnetic scattering models under a variety of boundary conditions, including Dirichlet, Neumann, impedance, and transmission types.

Continuation of Capillary Surfaces with Topological Change via the Van der Waals–Cahn–Hilliard Theory

Takashi Kagaya — 2026-03-06T08:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 506-531, April 2026.
Abstract. We study the capillary energy functional via the van der Waals–Cahn–Hilliard theory. Our study is motivated by how two droplets are connected as the volume increases. We deal with 2-dimensional case and the perturbation theory for the capillary energy functional and the continuous deformation of the critical point of the capillary energy functional allowing singularities when the area changes are discussed. Numerical computations based on the above theory are performed, and the results suggest that critical points consisting of two connected components and one connected component are connected by a continuous 1-parameter family of sets bounded by curves with a singularity, and hysteresis also can be seen in the dynamics.

Policy Iteration for Nonconvex Viscous Hamilton–Jacobi Equations

Xiaoqin Guo — 2026-03-12T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 532-556, April 2026.
Abstract. We study the convergence rates of policy iteration (PI) for nonconvex viscous Hamilton–Jacobi equations using a discrete space-time scheme, where both space and time variables are discretized. We analyze the case with an uncontrolled diffusion term, which corresponds to a possibly degenerate viscous Hamilton–Jacobi equation. We first obtain an exponential convergence result of PI for the discrete space-time schemes. We then investigate the discretization error.

Self-Similar Accumulation of Passive Particles Against Solute Gradients in One-Dimensional Channels or Porous Layers

Zhong Zheng — 2026-03-20T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 557-574, April 2026.
Abstract. We present a simple model to describe the self-similar accumulation/focusing of passive particles in one-dimensional channels or porous layers of infinite length under the influence of diffusiophoresis in the limit of an infinitely thin Debye layer. This occurs, e.g., when fresh water is injected into an open-end channel to displace salt water, which initially fills the channel and contains also passive particles. Two advective-diffusive equations are first provided to describe the coupled evolution of particle and solute concentrations. Two dimensionless control parameters are recognized that describe the influence of diffusiophoresis and particle diffusion over that of solute diffusion, respectively. The model predicts that accumulation of particles occurs toward the fluid-fluid interface when a solute gradient exists against the direction of the advective flow. Furthermore, the concentration profiles of both the solute and the particles can be described by self-similar solutions at intermediate times. Potential implications are also briefly remarked on tracer-based monitoring techniques in subsurface injection activities and microfluidic devices.

Ion Transport in Dipolar Medium II: A Local Dielectric Poisson–Nernst–Planck–Navier–Stokes Model

Sheng Gui — 2026-03-20T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 575-595, April 2026.
Abstract. The transport and distribution of charged particles in solvents are crucial in the study of many physical chemical and biological processes. Most continuum models introduce dielectric permittivity empirically, treating it as a constant or fitting it to experimental data. However, as is well known, physically it is mainly determined by local polarization. In our former work [S. Gui, B. Lu, and W. Yu, SIAM J. Appl. Math., 84 (5), pp. 2110–2131, 2024], we have proposed a set of ion transport and electrostatic models of the general electrolyte solution with a locally and mathematically strictly determined dielectric permittivity of the dipolar solvent under certain assumptions. In this paper, we further take into account the hydrodynamic effects on ion transport and propose a model of the incompressible conductive fluid by using an energetic variational approach, which could be called a local dielectric Poisson–Nernst–Planck–Navier–Stokes (LDPNP-NS) system. We also discuss the energy dissipation property of the derived LDPNP-NS equations. Finally, we show that the Onsager’s reciprocal relation holds for the electrokinetics.

The Behavior of the Direct Current Density at the Edge of Electrodes

Spyros Alexakis — 2026-04-02T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 596-614, April 2026.
Abstract. We study the shunt boundary condition for second order elliptic PDEs. A specific case of this is the PDE describing the electrostatic potential for a conductive body into which current is injected through electrodes that touch the boundary. We obtain the optimal description of the gradient of the electrostatic potential upon approach to the edge of the electrodes. This generalizes the classical Zaremba problem. The asymptotic description we obtain is then implemented to produce a substantial speed-up of numerical solvers for this boundary-value problem.

A Fourier-Based Inference Method for Learning Interaction Kernels in Particle Systems

Grigorios A. Pavliotis — 2026-04-02T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 615-643, April 2026.
Abstract. We consider the problem of inferring the interaction kernel of stochastic interacting particle systems from observations of a single particle. We adopt a semiparametric approach and represent the interaction kernel in terms of a generalized Fourier series. The basis functions in this expansion are tailored to the problem at hand and are chosen to be orthogonal polynomials with respect to the invariant measure of the mean-field dynamics. The generalized Fourier coefficients are obtained as the solution of an appropriate linear system whose coefficients depend on the moments of the invariant measure, and which are approximated from the particle trajectory that we observe. We quantify the approximation error in the Lebesgue space weighted by the invariant measure and study the asymptotic properties of the estimator in the joint limit as the observation interval and the number of particles tend to infinity, i.e., the joint large time–mean-field limit. We also explore the regime where an increasing number of generalized Fourier coefficients are needed to represent the interaction kernel. Our theoretical results are supported by extensive numerical simulations.

Complex Structure in the Endemic Equilibrium Set of an SIS Epidemic Patch Model with the Mass-Action Infection Mechanism

Rachidi B. Salako — 2026-04-03T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 644-674, April 2026.
Abstract. We investigate the structure of the endemic equilibrium (EE) set in a multipatch susceptible-infectious-susceptible (SIS) epidemic model with mass-action transmission mechanism. For the corresponding single-patch model, the basic reproduction number [math] completely determines the disease dynamics: a unique stable EE exists if and only if [math]. In contrast, the multipatch setting exhibits far more complex behavior. First, we show that as the dispersal rate of susceptible individuals [math] varies, the EE set consists of a finite union of disjoint curves. Under mild conditions, when [math], the closure of each curve forms a loop in the [math]-plane, where [math] denotes the total infected population at equilibrium. When [math], the EE set contains two distinct types of curves: bounded and unbounded. Moreover, the structure of the EE set as [math] tends to zero provides explicit spatial patterns of the EEs, offering insights into how restricting susceptible movement influences disease dynamics. Second, using [math] as the bifurcation parameter, we establish that the EE set forms a simple unbounded curve in the [math]-plane, which may exhibit an S-shape and undergo either a backward or forward transcritical bifurcation at [math]. These results refine and extend previous findings by revealing novel and intricate structures within the EE set. They underscore the interplay between population movement, total population size, and spatial heterogeneity, providing new insights into the long-term dynamics of infectious diseases.

Effective Medium Theory for Embedded Sound-Soft Obstacles in an Anisotropic Inhomogeneous Medium with Applications

Huaian Diao — 2026-04-13T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 675-698, April 2026.
Abstract. This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model commonly arises in the inverse scattering problem of simultaneously recovering the embedded obstacles and the surrounding medium. We propose a novel theoretical framework that demonstrates how embedded obstacles can be effectively approximated by an isotropic and lossy medium with specified physical parameters, wherein the total wave field exhibits decay properties related to these specified material parameters at the boundaries of the obstacles. This mathematical characterization of the wave in an effective medium model can be used to locate the underlying obstacles. Furthermore, we establish rigorous estimates to validate this approximation and provide a concrete example illustrating our theoretical results. Our proposed effective medium theory offers substantial applications within the context of the aforementioned inverse problem.

Two-Layer Flexural-Gravity Wave Propagation at a Blocking Point

Sunil Chandra Barman — 2026-04-17T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 699-729, April 2026.
Abstract. The first solution for the flexural-gravity wave propagation at the blocking and saddle points for a two-layer fluid is presented here. The compression on the plate-covered surface leads to wave blocking, where the group velocity vanishes. The blocking and saddle points are actually associated with a double and triple real root of the dispersion relation since the group velocity is the derivative of the dispersion relation. The solution in terms of eigenfunctions is restricted in the case of real and complex roots with multiplicity one of the dispersion relation. Now, we are able to overcome this restriction, and we newly obtain the complete solution for the velocity potential by establishing the orthogonal mode-coupling relation of the corresponding eigenfunctions for the flexural-gravity wave propagation at the blocking and saddle points using the Fourier transform. Further, the convergency of the newly derived solution at the blocking point is analyzed using the spectral representation of the associated eigenfunction. Next, we solve a simple model problem of flexural-gravity wave scattering by a crack in a floating ice sheet using the newly derived analytical solution at the blocking point. We show, by deriving the energy balance relation using Green’s theorem at the blocking point, that the validity of the energy identity is satisfied for the model problem. The ice sheet deflection and interface elevation are analyzed in the frequency domain at the blocking point, which is simulated in the time domain within and outside the blocking point frequencies.

Time-Delay Impact on the Stability of Kinetic Systems Linearly Conjugated to Complex Balanced Chemical Reaction Networks

Xiaoyu Zhang — 2026-04-20T07:00:00Z

SIAM Journal on Applied Mathematics, Volume 86, Issue 2, Page 730-750, April 2026.
Abstract. By utilizing the linear conjugacy relationship, the stability of a well-characterized system can be transferred to an unknown one. A key application lies in extending the stability of complex balanced (CB) systems to general systems linearly conjugate to them. However, introducing time delays to certain CB systems and their linearly conjugate counterparts may disrupt this conjugacy relationship, thereby hindering the transfer of stability properties. In this paper, we first establish several sufficient conditions to ensure the Lyapunov stability of the delayed version of systems linearly conjugated to CB systems. To further address the degenerated equilibrium in the stoichiometric compatibility class in such systems, we redefine the invariant sets of trajectories and extend the Lyapunov stability to achieve the local asymptotic stability with respect to the newly defined invariant sets. Illustrative examples, such as the PAK-1 network, are provided to validate the theoretical findings.