Abstract In this paper, the Hopf bifurcation and Turing instability for a mussel–algae model are investigated. Through analysis of corresponding kinetic system, existence stability conditions equilibrium type studied. Via center manifold theorem, sufficient in limit cycles obtained, respectively. addition, we find that strip patterns mainly induced by spot numerical simulations. These provide c...

This paper extends Turing analysis to standard recursive optimal control frameworks in economics and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics under optimal control over space creates (or destroys) spatial heterogeneity. We show how our approach reduces the analysis to a tractable extension of linearization methods applied to th...

This paper focuses on a strongly coupled specific ecological system consisting of two prey species and one predator. We explore unique positive equilibrium solution the that is globally asymptotically stable. Additionally, we show this remains locally linearly stable, even in presence diffusion. means does not follow classical Turing instability. However, it becomes unstable only when cross-dif...

We introduce a two-species fractional reaction-diffusion system to model activatorinhibitor dynamics with anomalous diffusion such as occurs in spatially inhomogeneous media. Conditions are derived for Turing instability induced pattern formation in these fractional activatorinhibitor systems whereby the homogeneous steady state solution is stable in the absence of diffusion, but becomes unstab...

We introduce a two-species fractional reaction-diffusion system to model activatorinhibitor dynamics with anomalous diffusion such as occurs in spatially inhomogeneous media. Conditions are derived for Turing-instability induced pattern formation in these fractional activatorinhibitor systems whereby the homogeneous steady state solution is stable in the absence of diffusion but becomes unstabl...

We hereby develop the theory of Turing instability for reaction-diffusion systems defined on complex networks assuming finite propagation. Extending to networked framework introduced by Cattaneo in 40's, we remove unphysical assumption infinite propagation velocity holding systems, thus allowing propose a novel view fine tuning issue and existing experiments. analytically prove that instability...

We analyse instabilities of standing pulses in reaction-diffusion systems that are caused by an absolute instability of the homogeneous background state. Specifically, we investigate the impact of pitchfork, Turing and oscillatory bifurcations of the rest state on the standing pulse. At a pitchfork bifurcation, the standing pulse continues through the bifurcation point where it selects precisel...