Turing Instability of Brusselator in the Reaction-Diffusion Network

Abstract

Turing instability constitutes a universal paradigm for the spontaneous generation of spatially organized patterns, especially in a chemical reaction. In this paper, we investigated the pattern dynamics of Brusselator from the view of complex networks and considered the interaction between diffusion and reaction in the random network. After a detailed theoretical analysis, we obtained the approximate instability region about the diffusion coefficient and the connection probability of the random network. In the meantime, we also obtained the critical condition of Turing instability in the network-organized system and found that how the network connection probability and diffusion coefficient affect the reaction-diffusion system of the Brusselator model. In the end, the reason for arising of Turing instability in the Brusselator with the random network was explained. Numerical simulation verified the theoretical results.

Pattern Dynamics in a Predator‐Prey Model with Diffusion Network

“…is paper theoretically derives Turing instability conditions [28][29][30][31] in a predator-prey network and carries out a detailed numerical study. We study the effects of diffusion and link probability on pattern formation in a random system.…”

Delay-induced self-organization dynamics in a prey-predator network with diffusion

“…Hopf and Turing bifurcations are obtained. When condition (11) holds, the network system always undergoes Hopf bifurcation and Turing bifurcation regardless of the network connection probability p [ Figures 3,4,5,6,and 11]. Namely, regardless of how the network nodes are connected, prey and predators will coexist, and the system will oscillate periodically.…”

“…Colorful patterns emerge from reaction-diffusion equations and can explain a wide variety of natural phenomena. Since Turing published his groundbreaking work [1], the Turing pattern has received increasing attention in biology, physics, chemicals, and other fields [2,3,4,5]. At present, it has been applied to more complex interdisciplinary subjects.…”

Stability, Chaos, and Bifurcation Analysis of a Discrete Chemical System

“…Zhao and Ma [10] have studied global and local bifurcations of a general Brusselator model. Ji and Shen [11] have studied the turing instability of a Brusselator in the reaction-diffusion network. Luo and Guo [12] have explored period-1 evolutions to chaos in a Brusselator.…”