Local Perception and Learning Mechanisms in Resource-Consumer Dynamics

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-05-13 DOI:10.1137/23m1598593

Qingyan Shi, Yongli Song, Hao Wang

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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 988-1010, June 2024.
Abstract. Spatial memory is key in animal movement modeling, but it has been challenging to explicitly model learning to describe memory acquisition. In this paper, we study novel cognitive consumer-resource models with different consumer learning mechanisms and investigate their dynamics. These models consist of two PDEs in composition with one ODE such that the spectrum of the corresponding linearized operator at a constant steady state is unclear. We describe the spectra of the linearized operators and analyze the eigenvalue problems to determine the stability of the constant steady states. We then perform bifurcation analysis by taking the perceptual diffusion rate as the bifurcation parameter. It is found that steady-state and Hopf bifurcations can both occur in these systems, and the bifurcation points are given so that the stability region can be determined. Moreover, rich spatial and spatiotemporal patterns can be generated in such systems via different types of bifurcation. Our effort establishes a new approach to tackling a hybrid model of PDE-ODE composition and provides a deeper understanding of cognitive movement-driven consumer-resource dynamics.

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资源-消费者动态中的局部感知和学习机制

SIAM 应用数学杂志》第 84 卷第 3 期第 988-1010 页，2024 年 6 月。摘要空间记忆是动物运动建模的关键，但如何明确地建立学习模型来描述记忆的获得一直是个挑战。本文研究了具有不同消费者学习机制的新型认知消费者-资源模型，并对其动力学进行了研究。这些模型由两个 PDE 与一个 ODE 组成，因此相应的线性化算子在恒定稳定状态下的频谱并不清楚。我们描述了线性化算子的频谱，并分析了特征值问题，以确定恒稳态的稳定性。然后，我们将感知扩散率作为分岔参数，进行分岔分析。结果发现，稳态和霍普夫分岔都可能发生在这些系统中，并给出了分岔点，从而确定了稳定区域。此外，通过不同类型的分岔，可以在这些系统中产生丰富的空间和时空模式。我们的研究为处理 PDE-ODE 复合模型提供了一种新方法，并加深了对认知运动驱动的消费者资源动力学的理解。

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

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.