The Effects of Stochasticity on Pattern Formation in a Space- and Time-Discrete Predator–Prey System with Strong Allee Effect in the Prey

2019 ◽  
Vol 81 (5) ◽  
pp. 1369-1393
Author(s):  
Joice Chaves Marques ◽  
Horst Malchow ◽  
Luiz Alberto Díaz Rodrigues ◽  
Diomar Cristina Mistro
Keyword(s):  
Pattern Formation ◽  
Allee Effect ◽  
Predator Prey ◽  
Space And Time ◽  
Prey System ◽  
Strong Allee Effect

Pattern formation in a space- and time-discrete predator–prey system with a strong Allee effect

2011 ◽  
Vol 5 (3) ◽  
pp. 341-362 ◽  
Author(s):  
Luiz Alberto Díaz Rodrigues ◽  
Diomar Cristina Mistro ◽  
Sergei Petrovskii
Keyword(s):  
Pattern Formation ◽  
Allee Effect ◽  
Predator Prey ◽  
Space And Time ◽  
Prey System ◽  
Strong Allee Effect

Spatiotemporal complexity of biological invasion in a space- and time-discrete predator–prey system with the strong Allee effect

2012 ◽  
Vol 9 ◽  
pp. 16-32 ◽  
Author(s):  
Diomar Cristina Mistro ◽  
Luiz Alberto Díaz Rodrigues ◽  
Sergei Petrovskii
Keyword(s):  
Biological Invasion ◽  
Allee Effect ◽  
Predator Prey ◽  
Space And Time ◽  
Prey System ◽  
Strong Allee Effect

scholarly journals Strong Allee effect in a diffusive predator–prey system with a protection zone

2014 ◽  
Vol 256 (1) ◽  
pp. 108-129 ◽  
Author(s):  
Renhao Cui ◽  
Junping Shi ◽  
Boying Wu
Keyword(s):  
Allee Effect ◽  
Predator Prey ◽  
Protection Zone ◽  
Prey System ◽  
Strong Allee Effect

Pattern Formation, Long-Term Transients, and the Turing–Hopf Bifurcation in a Space- and Time-Discrete Predator–Prey System

2010 ◽  
Vol 73 (8) ◽  
pp. 1812-1840 ◽  
Author(s):  
Luiz Alberto Díaz Rodrigues ◽  
Diomar Cristina Mistro ◽  
Sergei Petrovskii
Keyword(s):  
Hopf Bifurcation ◽  
Pattern Formation ◽  
Predator Prey ◽  
Space And Time ◽  
Prey System

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.

Predator–prey system with strong Allee effect in prey

2010 ◽  
Vol 62 (3) ◽  
pp. 291-331 ◽  
Author(s):  
Jinfeng Wang ◽  
Junping Shi ◽  
Junjie Wei
Keyword(s):  
Allee Effect ◽  
Predator Prey ◽  
Prey System ◽  
Strong Allee Effect

scholarly journals Dynamics in a diffusive predator-prey system with stage structure and strong allee effect

2020 ◽  
Vol 19 (2) ◽  
pp. 883-910
Author(s):  
Yuying Liu ◽  
◽  
Yuxiao Guo ◽  
Junjie Wei ◽  
◽  
...  
Keyword(s):  
Allee Effect ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Strong Allee Effect
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