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扩展的 - [公式：见文本] - 展开法与适形时空分数阶扩散捕食 - 食饵系统的新精确解

The extended-[Formula: see text]-expansion method and new exact solutions for the conformable space-time fractional diffusive predator-prey system.

作者信息

Wu Jie, Li Zhao, Tian Hao, Yang Zheng

机构信息

College of Computer Science, Chengdu University, Chengdu, 610106, China.

School of Mathematics, Sichuan University, Chengdu, 610065, China.

出版信息

Sci Rep. 2025 May 30;15(1):19053. doi: 10.1038/s41598-025-02856-5.

DOI:10.1038/s41598-025-02856-5
PMID:40447664
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC12125202/
Abstract

This paper explores the dynamics of the conformable space-time fractional diffusive predator-prey system using the extended-[Formula: see text]-expansion method. By incorporating negative exponents into the solution process, the study uncovers a broader set of exact solutions, providing deeper insights into the system's behavior. The analysis reveals how the solutions' singularities shift in response to variations in the fractional orders, with a movement towards the boundary as the fractional order decreases and towards the angle bisector of space-time as it approaches 1. Additionally, the paper identifies chaotic phenomena that emerge in the triangular solution when the fractional order is near 0.7, highlighting the sensitivity of the system to small changes in this range. Through graphical representations and solution analysis, the paper demonstrates how these fractional-order dynamics influence predator-prey interactions, offering valuable contributions to both mathematical biology and the study of fractional differential equations in complex systems.

摘要

本文运用扩展的[公式：见原文]展开法探究了适形时空分数阶扩散捕食-食饵系统的动力学特性。通过在求解过程中纳入负指数，该研究发现了更广泛的精确解集合，为深入了解系统行为提供了更深刻的见解。分析揭示了随着分数阶的变化，解的奇点如何移动，当分数阶减小时奇点向边界移动，而当分数阶接近1时向时空角平分线移动。此外，本文还识别出当分数阶接近0.7时在三角形解中出现的混沌现象，突出了系统在此范围内对微小变化的敏感性。通过图形表示和求解分析，本文展示了这些分数阶动力学如何影响捕食-食饵相互作用，为数学生物学以及复杂系统中的分数阶微分方程研究都做出了有价值的贡献。

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