Transition and coexistence of Turing pattern, Turing-like pattern and spiral waves in a discrete-time predator–prey model

IF 5.3 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Huimin Zhang , Jian Gao , Changgui Gu , Chuansheng Shen , Huijie Yang
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引用次数: 0

Abstract

Turing patterns and spiral waves, which are spatiotemporal ordered structures, are a common occurrence in complex systems, manifesting in a variety of forms. Investigations on these two types of patterns primarily concentrate on different systems or different parameter ranges, respectively. Turing’s theory, which postulates the presence of both a long-range inhibitor and a short-range activator, is used to explain the variety of Turing patterns in nature. Generally, Turing patterns are the result of Turing instability (including subcritical Turing instability), and research in this field is usually conducted within the parameter regions of Turing instability. Here, we observed the transition and coexistence phenomena of Turing pattern, Turing-like pattern and spiral wave, and discovered a mechanism for generating Turing-like patterns in discrete-time systems. Specifically, as the control parameter changes, the spiral wave gradually loses its dominant position and is eventually replaced by the Turing-like pattern, experiencing a state of coexistence of Turing/Turing-like pattern and spiral wave. The decrease in the move-state-effects results in the system’s incapacity to generate spiral waves, which are ultimately replaced by Turing/Turing-like patterns. Outside the parameter intervals of Turing instability, we obtained a type of Turing-like patterns in a discrete-time model. The patterns can be excited through the application of a strong impulse noise (exceeding a threshold) to a homogeneous stable state. Analysis reveals that the Turing-like patterns are the consequence of the competition between two stable states, and the excitation threshold is determined by the relative position of the states. Our findings shed light on the pattern formation for Turing/Turing-like patterns and spiral waves in discrete-time systems, and reflect the diversity of mechanisms behind emergence and self-organization.
离散时间捕食者--猎物模型中图灵模式、类图灵模式和螺旋波的过渡与共存
图灵模式和螺旋波是时空有序结构,是复杂系统中常见的现象,表现形式多种多样。对这两类模式的研究主要分别集中在不同的系统或不同的参数范围。图灵理论假设存在长程抑制剂和短程激活剂,用来解释自然界中的各种图灵模式。一般来说,图灵模式是图灵不稳定性(包括亚临界图灵不稳定性)的结果,该领域的研究通常在图灵不稳定性的参数区域内进行。在这里,我们观察到了图灵模式、类图灵模式和螺旋波的过渡和共存现象,并发现了离散时间系统中类图灵模式的产生机制。具体来说,随着控制参数的变化,螺旋波逐渐失去主导地位,最终被图灵样态所取代,出现图灵/图灵样态与螺旋波共存的状态。移动状态效应的减弱导致系统无法产生螺旋波,最终被图灵/类图灵图案所取代。在图灵不稳定性参数区间之外,我们在离散时间模型中获得了一种类图灵模式。通过对均质稳定状态施加强脉冲噪声(超过阈值),可以激发这种模式。分析表明,图灵样模式是两个稳定状态竞争的结果,而激发阈值由状态的相对位置决定。我们的发现揭示了离散时间系统中图灵/类图灵模式和螺旋波的模式形成,反映了涌现和自组织背后机制的多样性。
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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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