Pattern Formation Dynamics of Predator–Prey System with Hunting Cooperation in Predators

2019 ◽  
pp. 245-276
Author(s):  
Teekam Singh ◽  
Ramu Dubey
Keyword(s):  
Pattern Formation ◽  
Predator Prey ◽  
Prey System ◽  
Formation Dynamics

Pattern formation of a spatial predator–prey system

2012 ◽  
Vol 218 (22) ◽  
pp. 11151-11162 ◽  
Author(s):  
Gui-Quan Sun ◽  
Juan Zhang ◽  
Li-Peng Song ◽  
Zhen Jin ◽  
Bai-Lian Li
Keyword(s):  
Pattern Formation ◽  
Predator Prey ◽  
Prey System

Pattern formation in a diffusive predator–prey system with cross-diffusion effects

2020 ◽  
Vol 100 (4) ◽  
pp. 4045-4060
Author(s):  
Xiaoling Li ◽  
Guangping Hu ◽  
Shiping Lu
Keyword(s):  
Pattern Formation ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Prey System ◽  
Diffusion Effects

scholarly journals Neimark-Sacker-Turing Instability and Pattern Formation in a Spatiotemporal Discrete Predator-Prey System with Allee Effect

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Huayong Zhang ◽  
Xuebing Cong ◽  
Tousheng Huang ◽  
Shengnan Ma ◽  
Ge Pan
Keyword(s):  
Pattern Formation ◽  
Allee Effect ◽  
Initial Conditions ◽  
Turing Instability ◽  
Spatiotemporal Chaos ◽  
Closed Curves ◽  
Predator Prey ◽  
Prey System ◽  
Route To Chaos ◽  
The Rich

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.

Dynamics and pattern formation in a diffusive predator-prey system

2019 ◽  
Vol 475 (2) ◽  
pp. 1554-1577
Author(s):  
Hamed Norouzi ◽  
Ali Atabaigi ◽  
Ali Barati
Keyword(s):  
Pattern Formation ◽  
Predator Prey ◽  
Prey System

scholarly journals Turing pattern formation in a predator–prey system with cross diffusion

2014 ◽  
Vol 38 (21-22) ◽  
pp. 5022-5032 ◽  
Author(s):  
Zhi Ling ◽  
Lai Zhang ◽  
Zhigui Lin
Keyword(s):  
Pattern Formation ◽  
Turing Pattern ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Prey System
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