Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator–prey system

Abstract

A diffusive predator-prey system with Holling type-II predator functional response subject to Neumann boundary conditions is considered. Hopf and steady state bifurcation analysis are carried out in details. In particular we show the existence of multiple spatially non-homogeneous periodic orbits while the system parameters are all spatially homogeneous. Our results and global bifurcation theory also suggest the existence of loops of spatially non-homogeneous periodic orbits and steady state solutions. These results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulation.

Multiple bifurcations and spatiotemporal patterns for a coupled two-cell Brusselator model

“…In the following, we consider the general R-D system (2.1) with Neumann boundary condition on spatial domain Ω = (0, lπ), where From (H2), we can show that G satisfies the conditions of saddle-node bifurcation theorem of [21]. The proof is omitted, (see [18]). Therefore, under the assumption of (H2), saddle-node bifurcation occurs at b = b 0 .…”

“…In this section, by applying the results due to Shi and Wang [22] and Yi, Wei and Shi [18], we shall give the sufficient conditions for the global steady state bifurcation in the general R-D system (2.1). Then, by employing the technique introduced in Zhou and Mu [17], we investigate the steady state bifurcation for the coupled Brusselator model (1.2).…”

“…Yi, Wei and Shi [18,19] have investigated the Hopf and steady state bifurcations in a diffusion predator-prey model, and the multiple bifurcations in a diffusive bimolecular model, respectively.…”

Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth

“…In recent years, many authors investigate the diffusive predator-prey model with logistic prey growth rate [6][7][8][9][10] or strong Allee effect in prey [11]. It came out that this assumption is not realistic for a food-limited population under the effect of environmental toxicants.…”

Potencial para la conservación de la geodiversidad de los paisajes del Estado de Michoacán, México

“…Los ecólo-gos recientemente han comenzado a explorar cómo los cambios en la heterogeneidad del hábitat pueden influir en el funcionamiento del ecosistema al afectar importantes procesos como la producción primaria, la descomposición o el ciclo de nutrientes (Poggiale et al, 2005;Yi, et al, 2009;Peng, et al, 2013;Plexida, et al, 2014). La heterogeneidad del hábitat, además de tener una gran influencia en importantes procesos bióticos y abióticos, tales como alteración del paisaje y el movimiento de los organismos (Turner, 2005;Turner, et al, 2014), puede estar relacionada con la diversidad de especies, la resistencia y la función del ecosistema (Huston, 2014).…”