Results 61 to 70 of about 970 (177)

Neimark-Sacker-Turing Instability and Pattern Formation in a Spatiotemporal Discrete Predator-Prey System with Allee Effect

Discrete Dynamics in Nature and Society, 2018
A spatiotemporal discrete predator-prey system with Allee effect is investigated to learn its Neimark-Sacker-Turing instability and pattern formation.
Huayong Zhang, Xuebing Cong, Tousheng Huang, Shengnan Ma, Ge Pan   +4 more
doaj   +1 more source

Spatiotemporal Tipping Induced by Turing Instability and Hopf Bifurcation in a Population Ecosystem Model with the Fear Factor

Complexity, 2023
Population ecosystems can display the tipping points at which extinctions of species happens. To predict the appearance of tipping points and to understand their evolution mechanism are of uttermost importance for ecological balance.
Min Xiao, Gong Chen, Feilong Wang, Zunshui Cheng, Yi Yao   +4 more
doaj   +1 more source

Bifurcation Analysis of a Resource–Consumer System With Explicit Spatiotemporal Memory

Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.
ABSTRACT In ecological systems, animal movement is often influenced by memory and spatial cognition, especially in advanced species. This paper investigates the dynamics of a diffusive resource–consumer model incorporating explicit spatiotemporal distributed memory, where memory effects are modeled as distributed delays in both time and space.
Luhong Ye, Hao Wang
wiley   +1 more source

Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System [PDF]

Advances in Mathematical Physics, 2017
Noise is ubiquitous in a system and can induce some spontaneous pattern formations on a spatially homogeneous domain. In comparison to the Reaction-Diffusion System (RDS), Stochastic Reaction-Diffusion System (SRDS) is more complex and it is very difficult to deal with the noise function.
Qianiqian Zheng, Zhijie Wang, Jianwei Shen, Hussain Muhammad Ather Iqbal   +3 more
openaire   +3 more sources

A Thermodynamic Framework for Turing‐Type Instabilities in Porous Media: Part I Theory

Geochemistry, Geophysics, Geosystems, Volume 27, Issue 3, March 2026.
Abstract Pattern formation in geological materials is commonly described using analogies to Turing‐type reaction–diffusion systems, yet a unifying thermodynamic explanation remains elusive. Here we develop a multiscale, thermodynamically consistent framework for pattern‐forming instabilities in porous media undergoing coupled thermo–hydro–mechanical ...
Klaus Regenauer‐Lieb, Manman Hu, Qingpei Sun, Chong Liu, Zhennan Zhu, Victor Calo   +5 more
wiley   +1 more source

A Thermodynamic Framework for Turing‐Type Instabilities in Porous Media: Part II Applications

Geochemistry, Geophysics, Geosystems, Volume 27, Issue 3, March 2026.
Abstract Compaction bands, desiccation cracks, and melt segregation structures are geological patterns relying on the same fundamental manifestations of a universal Turing‐type instability mechanism, as predicted by the thermodynamically consistent reaction–cross‐diffusion framework developed in Part I (Regenauer‐Lieb et al., 2025, https://doi.org/10 ...
Klaus Regenauer‐Lieb, Manman Hu, Qingpei Sun, Chong Liu, Zhennan Zhu, Victor Calo   +5 more
wiley   +1 more source

A Nonlinear Cross-Diffusion Model for Disease Spread: Turing Instability and Pattern Formation

Mathematics
In this article, we propose a novel nonlinear cross-diffusion framework to model the distribution of susceptible and infected individuals within their habitat using a reduced SIR model that incorporates saturated incidence and treatment rates.
Ravi P. Gupta, Arun Kumar, Shristi Tiwari   +2 more
doaj   +1 more source

Using Shannon Entropy and Contagion Index to Interpret Pattern Self-Organization in a Dynamic Vegetation-Sand Model

IEEE Access, 2020
Vegetation pattern is one of the most important self-organized patterns in ecological systems. The formation mechanism of vegetation patterns has been attributed to dynamic bifurcations, while from the external perspective, the regularity of patterns ...
Feifan Zhang, Lei Yao, Wenjiao Zhou, Qinjing You, Huayong Zhang   +4 more
doaj   +1 more source

Well‐Posedness and Pattern Formation in a Two‐Species Reaction–Diffusion System with Nonlocal Perception

Studies in Applied Mathematics, Volume 156, Issue 2, February 2026.
ABSTRACT Nonlocal perceptual cues, such as visual, auditory, and olfactory signals, profoundly influence animal movement and the emergence of ecological patterns. To capture these effects, we introduce a two‐species reaction–diffusion system with mutual nonlocal perception on a two‐dimensional periodic domain.
Yaqi Chen, Ben Niu, Hao Wang
wiley   +1 more source

Spatial Complexity of a Predator-Prey Model with Holling-Type Response

Abstract and Applied Analysis, 2014
We focus on a spatially extended Holling-type IV predator-prey model that contains some important factors, such as noise (random fluctuations), external periodic forcing, and diffusion processes.
Lei Zhang, Zhibin Li
doaj   +1 more source