Turing Instability in Inhomogeneous Arrays of Diffusively Coupled Reactors

2004 ◽  
Vol 108 (12) ◽  
pp. 2225-2231 ◽  
Author(s):  
Werner Horsthemke ◽  
Peter K. Moore
Keyword(s):  
Turing Instability ◽  
Coupled Reactors

scholarly journals Dynamical study of infochemical influences on tropic interaction of diffusive plankton system

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Satish Kumar Tiwari ◽  
Ravikant Singh ◽  
Nilesh Kumar Thakur
Keyword(s):  
Dimethyl Sulfide ◽  
Algal Bloom ◽  
Turing Instability ◽  
Model System ◽  
Ode Model ◽  
Estuarine Ecosystem ◽  
Dynamical Study ◽  
Oscillatory Dynamics ◽  
The Stability ◽  
Microzooplankton Grazing

AbstractWe propose a model for tropic interaction among the infochemical-producing phytoplankton and non-info chemical-producing phytoplankton and microzooplankton. Volatile information-conveying chemicals (infochemicals) released by phytoplankton play an important role in the food webs of marine ecosystems. Microzooplankton is an ecologically important grazer of phytoplankton for coexistence of a large number of phytoplankton species. Here, we discuss how information transferred by dimethyl sulfide shapes the interaction of phytoplankton. Phytoplankton deterrents may lead to propagation of IPP bloom. The interaction between IPP and microzooplankton follows the Beddington–DeAngelis-type functional response. Analytically, we discuss boundedness, stability and Turing instability of the model system. We perform numerical simulation for temporal (ODE model) as well as a spatial model system. Our numerical investigation shows that microzooplankton grazing refuse of IPP leads to oscillatory dynamics. Increasing diffusion coefficient of microzooplankton shows Turing instability. Time evolution also plays an important role in the stability of system dynamics. The results obtained in this paper are useful to understand the dominance of algal bloom in coastal and estuarine ecosystem.

Exact noise in three-region coupled reactors

1995 ◽  
Vol 29 (3-4) ◽  
pp. 265-297
Author(s):  
P.B. Pérez ◽  
J.R. Sheff
Keyword(s):  
Coupled Reactors

Multiscale Modeling of ZnO Nanoparticle Synthesis: Chemical Kinetics and Turing Instability

2021 ◽  
pp. 102748
Author(s):  
Raúl Mendoza Báez ◽  
Marco A. Morales ◽  
Adan Luna Flores ◽  
Ricardo Agustín Serrano
Keyword(s):  
Chemical Kinetics ◽  
Multiscale Modeling ◽  
Nanoparticle Synthesis ◽  
Turing Instability ◽  
Zno Nanoparticle

scholarly journals Complex Dynamical Behavior of a Predator-Prey System with Group Defense

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jianglin Zhao ◽  
Min Zhao ◽  
Hengguo Yu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Basis ◽  
Dynamical Behavior ◽  
Turing Instability ◽  
Equilibrium Density ◽  
Prey Refuge ◽  
Predator Prey ◽  
Prey System ◽  
Group Defense ◽  
Complex Dynamical Behavior

A diffusive predator-prey system with prey refuge is studied analytically and numerically. The Turing bifurcation is analyzed in detail, which in turn provides a theoretical basis for the numerical simulation. The influence of prey refuge and group defense on the equilibrium density and patterns of species under the condition of Turing instability is explored by numerical simulations, and this shows that the prey refuge and group defense have an important effect on the equilibrium density and patterns of species. Moreover, it can be obtained that the distributions of species are more sensitive to group defense than prey refuge. These results are expected to be of significance in exploration for the spatiotemporal dynamics of ecosystems.

Turing Instability and Hopf Bifurcation in Cellular Neural Networks

2021 ◽  
Vol 31 (08) ◽  
pp. 2150143
Author(s):  
Zunxian Li ◽  
Chengyi Xia
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Turing Instability ◽  
Cellular Neural Networks ◽  
Bifurcation Theorem ◽  
Decoupling Method ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Approximate Expressions ◽  
Zero Equilibrium

In this paper, we explore the dynamical behaviors of the 1D two-grid coupled cellular neural networks. Assuming the boundary conditions of zero-flux type, the stability of the zero equilibrium is discussed by analyzing the relevant eigenvalue problem with the aid of the decoupling method, and the conditions for the occurrence of Turing instability and Hopf bifurcation at the zero equilibrium are derived. Furthermore, the approximate expressions of the bifurcating periodic solutions are also obtained by using the Hopf bifurcation theorem. Finally, numerical simulations are provided to demonstrate the theoretical results.

scholarly journals Turing instability in two-patch predator-prey population dynamics

2018 ◽  
Vol 18 (03) ◽  
pp. 255-261
Author(s):  
Ali Al-Qahtani ◽  
Aesha Almoeed ◽  
Bayan Najmi ◽  
Shaban Aly
Keyword(s):  
Population Dynamics ◽  
Turing Instability ◽  
Prey Population ◽  
Predator Prey

Pattern Dynamics in a Spatial Predator–Prey Model with Nonmonotonic Response Function

2018 ◽  
Vol 28 (06) ◽  
pp. 1850077 ◽  
Author(s):  
Xiaoling Li ◽  
Guangping Hu ◽  
Zhaosheng Feng
Keyword(s):  
Response Function ◽  
Turing Instability ◽  
Spatiotemporal Pattern ◽  
Weakly Nonlinear ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Pattern Dynamics ◽  
Spatial Systems ◽  
Different Types ◽  
Selection Of

In this paper, we study a diffusive predator–prey system with the nonmonotonic response function. The conditions on Hopf bifurcation and Turing instability of spatial systems are obtained. Near the Turing bifurcation point we apply the weakly nonlinear analysis to derive the amplitude equations of stationary pattern, to investigate the selection of spatiotemporal pattern. It shows that different types of patterns will occur in the model under various conditions. Numerical simulations agree well with our theoretical analysis when control parameters are in the Turing space. This study may provide some deep insights into the formation and selection of patterns for diffusive predator–prey systems.

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