Qualitative study for the system of waste plastic management in the ocean: A discrete-time deterministic model

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-17 DOI:10.1016/j.cnsns.2025.108617

Mahmood Parsamanesh , Mehmet Gümüş

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引用次数: 0

Abstract

Ocean waste is a serious environmental problem affecting marine ecosystems and marine life. A large portion of this waste consists of recyclable materials. If managed correctly, it provides both economic and environmental benefits. By using mathematical models, it is possible to predict the spread of these wastes and develop strategies. In this paper, a discrete-time compartmental model is introduced for the cycle of processing the waste plastic management in the ocean. The model comprises three compartments plastic waste, marine debris, and recycled materials. A system of difference equations is formulated for this process according to the transmissions of materials between compartments. Then two equilibria for the model are obtained; the marine debris-free equilibrium point and the marine debris-included equilibrium point. Also, the basic reproduction number for the model is given, then its stability is investigated and stated in terms of this quantity. Furthermore, the bifurcations of the model including transcritical, period-doubling, and Neimark–Sacker bifurcation, are studied and the conditions for their occurrence are given. The obtained theoretical results are verified via several examples and simulations.

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海洋废塑料管理系统的定性研究：一个离散时间确定性模型

海洋废弃物是影响海洋生态系统和海洋生物的严重环境问题。这种废物的很大一部分是可回收材料。如果管理得当，它可以提供经济和环境效益。通过使用数学模型，可以预测这些废物的扩散并制定策略。本文介绍了海洋废塑料处理循环管理的离散时间分区模型。该模型由三个隔间组成：塑料垃圾、海洋垃圾和回收材料。根据物料在车厢间的传输，建立了这一过程的差分方程组。得到了模型的两个平衡点；无海洋垃圾均衡点和含海洋垃圾均衡点。同时，给出了模型的基本再现数，并以此量考察了模型的稳定性。进一步研究了模型的跨临界分岔、周期加倍分岔和neimmark - sacker分岔，并给出了它们发生的条件。通过算例和仿真验证了所得理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.