Neimark-Sacker-Turing instability and pattern formation in a spatiotemporal discrete predator-prey system with Allee effect
type: Item
instance of: scholarly article
title: Neimark-Sacker-Turing instability and pattern formation in a spatiotemporal discrete predator-prey system with Allee effect
zbMATH Open document ID: 1417.92165
DOI: 10.1155/2018/8713651
author: Huayong Zhang
author: Xuebing Cong
author: Tousheng Huang
author: Shengnan Ma
author: Ge Pan
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-20T00:00:00Z
review text: Summary: A spatiotemporal discrete predator-prey system with Allee effect is investigated to learn its Neimark-Sacker-Turing instability and pattern formation. Based on the occurrence of stable homogeneous stationary states, conditions for Neimark-Sacker bifurcation and Turing instability are determined. Numerical simulations reveal that Neimark-Sacker bifurcation triggers a route to chaos, with the emergence of invariant closed curves, periodic orbits, and chaotic attractors. The occurrence of Turing instability on these three typical dynamical behaviors leads to the formation of heterogeneous patterns. Under the effects of Neimark-Sacker-Turing instability, pattern evolution process is sensitive to tiny changes of initial conditions, suggesting the occurrence of spatiotemporal chaos. With application of deterministic initial conditions, transient symmetrical patterns are observed, demonstrating that ordered structures can exist in chaotic processes. Moreover, when local kinetics of the system goes further on the route to chaos, the speed of symmetry breaking becomes faster, leading to more fragmented and more disordered patterns at the same evolution time. The rich spatiotemporal complexity provides new comprehension on predator-prey coexistence in the ways of spatiotemporal chaos.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 39A60
zbMATH DE Number: 7026715
Wikidata QID: Q115521943
describes a project that uses: PRED_PREY
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8713651
OpenAlex ID: W2810899077
cites work: Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB
cites work: Pattern formation of a spatial predator-prey system
cites work: Hopf and steady state bifurcation analysis in a ratio-dependent predator-prey model
cites work: Complex patterns in a space- and time-discrete predator-prey model with Beddington-DeAngelis functional response
cites work: Wave of chaos and pattern formation in spatial predator-prey systems with Holling type IV predator response
cites work: Dynamics and pattern formation in a diffusive predator-prey system with strong Allee effect in prey
cites work: Pattern dynamics in a spatial predator-prey system with Allee effect
cites work: Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity
cites work: Turing pattern formation in a predator-prey system with cross diffusion
cites work: The chemical basis of morphogenesis
cites work: Nonlocal interaction driven pattern formation in a prey-predator model
cites work: Period-doubling of kink-antikink patterns, quasiperiodicity in antiferro-like structures and spatial intermittency in coupled logistic lattice. Towards a prelude of a ``field theory of chaos''.
cites work: Transition from torus to chaos accompanied by frequency lockings with symmetry breaking. In connection with the coupled-logistic map.
cites work: Spatiotemporal intermittency in coupled map lattices
cites work: Bifurcation, chaos and pattern formation in a space- and time-discrete predator-prey system
cites work: Spatiotemporal complexity of a discrete space-time predator-prey system with self- and cross-diffusion
cites work: Bifurcation analysis of a discrete-time ratio-dependent predator-prey model with Allee effect
cites work: Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect.
cites work: Oscillation deduced from the Neimark-Sacker bifurcation in a discrete dual Internet congestion control algorithm
cites work: Spiral patterns near Turing instability in a discrete reaction diffusion system
description: scientific article; zbMATH DE number 7026715