Dynamics of a diffusive model in the anaerobic digestion process

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-12-16 DOI:10.1016/j.cnsns.2024.108523

Lin Wang, Linlin Bu, Jianhua Wu

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引用次数: 0

Abstract

The joined effects of syntrophic relationship and substrate inhibition are considered in a diffusive model of the anaerobic digestion process. We first establish the existence and structure of coexistence solutions for the system in different growth rate parameter ranges. Numerical results suggest that the coexistence solutions of the system undergo double bifurcation in the suitable range of growth rate coefficients. The time evolution of solutions simulated in a high-dimensional space further demonstrates the multiplicity, as well as the magnitude and the spatial distribution of solutions for the system, offering valuable insights for future theoretical analysis. The effect of substrate inhibition on species coexistence is analyzed, and the result reveals that species cannot coexist when the substrate inhibition is sufficiently large. Finally, the dynamic behavior of the system is investigated from both theoretical and numerical perspectives, including the global attractivity of semi-trivial steady-state solutions and the uniform persistence of the system.

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厌氧消化过程中扩散模型的动力学

在厌氧消化过程的扩散模型中考虑了共生关系和底物抑制的联合效应。首先建立了系统在不同生长速率参数范围内共存解的存在性和结构。数值结果表明，系统的共存解在适当的增长率系数范围内发生双分岔。在高维空间中模拟的解的时间演化进一步证明了系统解的多样性、大小和空间分布，为未来的理论分析提供了有价值的见解。分析了底物抑制对物种共存的影响，结果表明，当底物抑制足够大时，物种不能共存。最后，从理论和数值两方面研究了系统的动力学行为，包括半平凡稳态解的全局吸引性和系统的一致持续性。

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.