Aug 2026· Mathematics· Vol 14, pp. 2879· 0 citations· 32 references
Abstract
We study a reaction–diffusion model for population–toxin interactions on a two-dimensional torus, where avoidance is driven by a nonlocal average of toxin-related memory. The variables represent population density, toxin concentration, and a phenomenological information field generated by population–toxin encounters. This information diffuses, decays, and enters the taxis term through convolution with a perceptual kernel. We prove local well-posedness, global existence and uniform boundedness, and give sufficient conditions for exponential convergence to either the positive equilibrium or the toxin-only equilibrium. Numerical simulations with two perceptual radii yield stripe and spot patterns, illustrating that the sensing scale can alter spatial organization. These simulations do not establish an effect on population persistence and should be viewed as hypotheses for empirical study.
This paper investigates a time-periodic, spatiotemporally heterogeneous competition-diffusion system, where two species have different intrinsic growth rates but equal total resources per period. Using asymptotic analysis and principal eigenvalue theory, we systematically examine its dynamics. When both diffusion rates...
We incorporate stochastic fluctuations into an epidemic-behavior coevolution model and study its threshold dynamics and stationary distributions. By introducing the stochastic basic reproduction number R0σ, the behavioral threshold d, and two potential infection proportions RPσ,1 and RPσ,2, we establish conditions for...
Huan Yang, Sanyi Tang, Lin Wang· Journal of Theoretical Biolo...· 0 citations
In this paper, we develop a unified framework based on generalized principal eigenvalues to study spreading speeds in time‐heterogeneous nonlocal diffusion models. First, for time‐heterogeneous environments with a positive uniform mean value, we investigate the properties and interrelationships of three types of genera...
The model produces the so-called "Turing-before-Tipping"phenomenon demonstrating that the arrangement into spatial patterns is an effective resilience mechanism against harsh conditions, and there is a kernel-dependent dichotomy in pattern behavior.
Olivia Clifton, Stephanie Dodson, Daniel B. Cooney· 1 citation
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