相关论文: Stability and bifurcations in a model of antigenic…

A retrovirus dynamic model is proposed. We pay attention to the case when viral pathogenicity is low and the infected cells are able to reproduce. Using Lyapunov function method we study stability properties of an inner equilibrium of the…

We consider an epidemiological model that includes waning and boosting of immunity. Assuming that repeated exposure to the pathogen fully restores immunity, we derive an SIRS-type model with discrete and distributed delays. First we prove…

In this note we present a study of the solutions associated to a particular spatial extension of the Rosenzweig-MacArthur model for predator and prey. The analysis presented here shows that positive steady state solutions emerge via a…

We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal…

This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform…

We investigate the structure and stability of the steady states for a bacterial colony model with density-suppressed motility. We treat the growth rate of bacteria as a bifurcation parameter to explore the local and global structure of the…

We comment on the recent work by Yamaguchi and Barr\'e [Phys. Rev. E 107, 054203 (2023)], which uses linear stability analysis of the Vlasov equation to characterize phase transitions in a generalized Hamiltonian Mean Field (gHMF) model. By…

A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…

An age-structured predator-prey system with diffusion and Holling-Tanner-type nonlinearities is considered. Regarding the intensity of the fertility of the predator as bifurcation parameter, we prove that a branch of positive coexistence…

A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are…

We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold…

We study certain significant properties of the equilibrium configurations of a rigid body subject to an undamped elastic restoring force, in the stream of a viscous liquid in an unbounded 3D domain. The motion of the coupled system is…

The existence of a die-out threshold (different from the classic disease-invasion one) defining a region of slow extinction of an epidemic has been proved elsewhere for susceptible-aware-infectious-susceptible models without awareness…

The spatiotemporal patterns of a reaction diffusion mussel-algae system with a delay subject to Neumann boundary conditions is considered. The paper is a continuation of our previous studies on delay-diffusion mussel-algae model. The global…

We examine the effect of a slowly-varying time-dependent parameter on invasion fronts for which an unstable homogeneous equilibrium is invaded by either another homogeneous state or a spatially periodic state. We first explain and motivate…

The paper is devoted to the study of the asymptotic behaviour of Moran process in random environment, say random selection. In finite population, the Moran process may be degenerate in finite time, thus we will study its limiting process in…

The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter $\epsilon$. Under suitable assumptions the solution of the…

We are interested in the long-time asymptotic behavior of growth-fragmentation equations with a nonlinear growth term. We present examples for which we can prove either the convergence to a steady state or conversely the existence of…

In this work we identify and investigate a novel bifurcation in conserved systems. This secondary bifurcation stops active phase separation in its nonlinear regime. It is then either replaced by an extended, system-filling, spatially…

This study examines the behavior of solutions in a multi-patch epidemic model that includes a saturation incidence mechanism. When the fatality rate due to the disease is not null, our findings show that the solutions of the model tend to…