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数学生态学分数捕食者

花匠小妙招
2025-02-17 03:49

数学生态学分数捕食者-猎物模型的复杂动态行为

摘要

本文提出了一个捕食者-猎物数学模型，其中捕食者种群分为两个阶段：成熟（成年）阶段和幼年阶段。因此，捕食者-被捕食者模型中包含三个耦合常微分方程，三个状态变量分别是成熟捕食者、幼年捕食者和猎物。该捕食者-猎物模型用卡普托、卡普托-法布里齐奥（C-F）和分数-分数（F-F）算子来描述。分数阶捕食者-猎物动力学模型有助于在分数算子的帮助下描述记忆和遗传特性的功效（有用性、有效性）。我们利用定点公设研究了具有 C-F 和分数-分数（F-F）导数的解的唯一性和存在性。该模型还表现出基于非线性函数分析的乌拉姆稳定性。利用相位肖像对非整数捕食者-猎物模型进行了数值和行为分析。带有卡普托-法布里齐奥（C-F）和分形-分数（F-F）算子的捕食者-猎物系统分别通过亚当斯-巴什福斯方案和新的预测器-校正器方案进行了数值求解。通过对捕食者-猎物模型的数值模拟分析，我们说明了这些方法的有效性和适用性。数值模拟使用 Matlab 编程进行。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

Complex dynamic behaviour on fractional predator–prey model of mathematical ecology

In this paper, we present a mathematical predator–prey model in which the predator population is divided into two stages: mature (adult) stage and juvenile stage. Therefore, three coupled ordinary differential equations are incorporated in the predator–prey model with three state variables; mature predator, juvenile predator and prey. This predator–prey model is described in terms of Caputo, Caputo–Fabrizio (C–F) and fractal–fractional (F–F) operators. The fractional order predator–prey dynamical model helps to describe the efficacy (usefulness, effectiveness) of memory and hereditary properties with the help of fractional operators. We have investigated the uniqueness and existence of solutions with C–F and fractal–fractional (F–F) derivatives using the fixed point postulate. This model also exhibits Ulam’s type of stability based on nonlinear functional analysis. Numerical and behavioral analyses of the non-integer predator–prey model have been carried out using phase portraits. The predator–prey system with Caputo–Fabrizio (C–F) and fractal–fractional (F–F) operators have been solved numerically via the Adams-Bashforth scheme and new predictor–corrector scheme respectively. In an analysis of numerical simulations of predator–prey models, we have illustrated the effectiveness and applicability of these methods. Numerical simulations were performed using Matlab programming.

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来源期刊

Journal of Applied Mathematics and Computing

期刊介绍： JAMC is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical computing. Major areas, such as numerical analysis, discrete optimization, linear and nonlinear programming, theory of computation, control theory, theory of algorithms, computational logic, applied combinatorics, coding theory, cryptograhics, fuzzy theory with applications, differential equations with applications are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.

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