Abstract. In real-world ecosystem, studies on the mechanisms of spatiotemporal pattern formation in a system of interacting populations deserve special attention for its own importance in contemporary theoretical ecology. The present investigation deals with the spatial dynamical system of a two-dimensional continuous diffusive predator–prey model involving the influence of intra-species compet...

In this paper, we investigate the emergence of a predator-prey system with Ivlevtype functional response and reaction-diffusion. We study how diffusion affects the stability of predator-prey coexistence equilibrium and derive the conditions for Hopf and Turing bifurcation in the spatial domain. Based on the bifurcation analysis, we give the spatial pattern formation, the evolution process of th...

Fronts are traveling waves in spatially extended systems that connect two different spatially homogeneous rest states. If the rest state behind the front undergoes a supercritical Turing instability, then the front will also destabilize. On the linear level, however, the front will be only convectively unstable since perturbations will be pushed away from the front as it propagates. In other wo...

Abstract The classical Cahn–Hilliard (CH) equation corresponds to a gradient dynamics model that describes phase decomposition in binary mixture. In the spinodal region, an initially homogeneous state spontaneously decomposes via large-scale instability into drop, hole or labyrinthine concentration patterns of typical structure length followed by continuously ongoing coarsening process. Here, w...

In this paper, we consider a general time-space discrete host-parasitoid model with the periodic boundary conditions. We analyzed and obtained some usual conditions, such as Turing instability occurrence, Flip bifurcation Neimark-Sacker occurrence. also find several multiple phenomena, 1 : 2 Resonance, Neimark-Sacker-Flip bifurcation, Neimark-Sacker-Neimark-Sacker Neimark-Sacker-Flip-Flip induc...

In this paper, a water-vegetation model with the infiltration feedback effect is considered. Firstly, through linear stability analysis, we get parameter area where Turing instability can occur. Next, by maximum principle, priori estimates for positive steady-state solutions are obtained and sufficient conditions nonexistence of nonconstant solution given. Moreover, bifurcations at both simple ...

In this paper, we study the Turing–Hopf bifurcation in predator–prey model with cross-diffusion considering individual behaviour and herd transition of prey population subject to homogeneous Neumann boundary condition. Firstly, non-negativity boundedness solutions corresponding temporal model, spatiotemporal existence priori without cross-diffusion. Then by analysing eigenvalues characteristic ...

Arising from modulation instability, Turing rolls in optical Kerr microresonators have been used the generation of frequency combs and synthesis microwave terahertz frequencies. In this work, by applying electro-optic on terahertz-frequency rolls, we implement division with a microcomb to synthesize variable low-noise signals. We also actively stabilize oscillations reference via intracavity po...

The existence and stability of localized patterns of criminal activity are studied for the reaction-diffusion model of urban crime that was introduced by Short et. al. [Math. Models. Meth. Appl. Sci., 18, Suppl. (2008), pp. 1249–1267]. Such patterns, characterized by the concentration of criminal activity in localized spatial regions, are referred to as hot-spot patterns and they occur in a par...