Related papers: Time-dependent localized patterns in a predator-pr…
The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
In this paper we extend previous results on convergent perturbative solutions of the Schroedinger equation of a class of periodically time-dependent two-level systems. The situation treated here is particularly suited for the investigation…
Environmental enrichment can destabilize predator--prey coexistence through a Hopf bifurcation, yet real ecosystems are finite and intrinsically stochastic. We investigate how mechanistically derived demographic noise shapes near-Hopf…
We identify a geometric principle governing the location of Hopf and Bogdanov--Takens bifurcations in planar predator--prey systems. The prey coordinate of any coexistence equilibrium undergoing such a bifurcation lies between consecutive…
We investigate a specific reaction-diffusion system that admits a monostable pulled front propagating at constant critical speed. When a small parameter changes sign, the stable equilibrium behind the front destabilizes, due to essential…
It is proved the existence and uniqueness of the global positive solution to the system of stochastic differential equations describing a non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower and Holling-type…
Fluids subject to both thermal and compositional variations can undergo doubly diffusive convection when these properties both affect the fluid density and diffuse at different rates. A variety of patterns can arise from these…
We study a spatial predator-prey model in which prey can enter a protection zone (refuge) inaccessible to predators, while predators exhibit directed movement toward prey-rich regions. The directed movement is modeled by a far-sighted…
We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classic differential equation models with…
In this work, we study the dynamics of a spatially heterogeneous single population model with the memory effect and nonlinear boundary condition. By virtue of the implicit function theorem and Lyapunov-Schmidt reduction, spatially…
In this paper, we analyse a recently proposed predator-prey model with ratio dependence and Holling type III functional response, with particular emphasis on the dynamics close to extinction. By using Briot-Bouquet transformation we…
A novel analysis of homogeneous nucleation of dislocations in sheared two-dimensional crystals described by periodized discrete elasticity models is presented. When the crystal is sheared beyond a critical strain $F=F_{c}$, the strained…
We explore a diffusive predator-prey system that incorporates the fear effect in advective environments. Firstly, we analyze the eigenvalue problem and the adjoint operator, considering Constant-Flux and Dirichlet (CF/D) boundary…
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…
For a Selkov--Schnakenberg model as a prototype reaction-diffusion system on two dimensional domains we use the continuation and bifurcation software pde2path to numerically calculate branches of patterns embedded in patterns, for instance…
A wide variety of stationary or moving spatially localized structures is present in evolution problems on unbounded domains, governed by higher-than-second-order reversible spatial interactions. This work provides a generic unfolding in one…
We study numerically the cubic-quintic-septic Swift-Hohenberg (SH357) equation on bounded one-dimensional domains. Under appropriate conditions stripes with wave number $k\approx 1$ bifurcate supercritically from the zero state and form…
In this paper we explore the eco-evolutionary dynamics of a predator-prey model, where the prey population is structured according to a certain life history trait. The trait distribution within the prey population is the result of interplay…