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

机译:Neimark-ancker-TING稳定性和图案形成,在天空间离散的捕食者 - 猎物系统中的效果

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摘要

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.
机译:调查了一种带有Allee效果的时空离散的捕食者 - 猎物系统,以了解其Neimark-Sacker-Tures稳定性和模式形成。基于稳定的均匀静止状态的发生,确定了内马克解锁器分叉和稳定性的条件。数值模拟表明,Neimark-Sacker分叉触发到混沌的路线,出现不变的闭合曲线,周期性轨道和混沌吸引子。在这三种典型动力学行为上进行无稳定性的发生导致形成异质图案。在Neimark-Sacker-TINGE的影响下,模式演化过程对初始条件的微小变化敏感,表明时尚混沌的发生。通过应用确定性初始条件,观察到瞬态对称图案,证明有序结构可以存在于混沌过程中。此外,当系统的局部动力学进一步进入混沌的路线时,对称性断裂的速度变得更快,导致相同的演化时间更加碎片和更无序的模式。丰富的时空复杂性为捕食者 - 猎物共存的新理解提供了时尚混乱的方式。

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