Effects of extra resource and harvesting on the pattern formation for a predation system

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-10-04 DOI:10.1016/j.cnsns.2024.108381

Yunfeng Jia , Jingjing Wang

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Abstract

We deal with a reaction–diffusion predation system with extra resource provided to predator and harvesting on prey. We first discuss the long-time behaviors of parabolic system, including the dissipativeness and persistence of positive solutions. It is shown that under certain constraints of harvesting, the quality of extra resource, the predation and transition rates of predator, the dissipativeness is compatible with persistence. Secondly, some properties of steady-state system are investigated, mainly including the existence of non-constant positive solutions, Turing and steady-state bifurcation phenomena. It is found that the extra resource, prey harvesting and diffusion have significant impacts on the pattern formations. Furthermore, some numerical simulations on Turing patterns and steady-state bifurcation solutions are performed to illustrate the theoretical analysis. We observe that when the quantity of extra resources is low, changes in the quality of extra resources can lead to significant changes in the spatial distribution of species, which is in sharp contrast to the case of high quantity of extra resource. Additionally, we conclude that different diffusion rates of predator can lead to different spatial patterns for the system.

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额外资源和收获对捕食系统模式形成的影响

我们研究的是一个反应扩散捕食系统，捕食者获得额外资源，猎物获得收获。我们首先讨论了抛物线系统的长期行为，包括正解的离散性和持久性。结果表明，在一定的收获、额外资源质量、捕食者捕食率和过渡率约束下，耗散性与持久性是一致的。其次，研究了稳态系统的一些特性，主要包括非恒定正解的存在、图灵和稳态分岔现象。研究发现，额外资源、猎物捕获和扩散对模式形成有显著影响。此外，还对图灵模式和稳态分叉解进行了一些数值模拟，以说明理论分析。我们发现，当额外资源数量较少时，额外资源质量的变化会导致物种空间分布的显著变化，这与额外资源数量较多的情况形成鲜明对比。此外，我们还得出结论，不同的捕食者扩散率会导致系统出现不同的空间模式。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.