Results 51 to 60 of about 168,933 (177)
Spatiotemporal dynamics of a diffusive predator-prey model with delay and Allee effect in predator
Mathematical Biosciences and Engineering, 2023 It has been shown that Allee effect can change predator-prey dynamics and impact species persistence. Allee effect in the prey population has been widely investigated. However, the study on the Allee effect in the predator population is rare.
Fang Liu, Yanfei Du
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Spatiotemporal complexity of a ratio-dependent predator-prey system
, 2007 In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten-type functional response and reaction-diffusion. We derive the conditions for Hopf, Turing and Wave bifurcation on a spatial domain.
A. M. Turing +12 more
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Instabilities and Patterns in Coupled Reaction-Diffusion Layers
, 2012 We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric ...
Catlla, Anne J. +2 more
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Diffusive Resource–Consumer Dynamics With the Simplest Learning Mechanism and Nonlocal Memory Usage
Mathematical Methods in the Applied Sciences, Volume 48, Issue 18, Page 16433-16444, December 2025.ABSTRACT To describe cognitive consumers' movement, we study a diffusive resource–consumer model with nonlocal memory usage described by a system of parabolic equations, which is coupled with spatial memory dynamics described by a linear learning equation.
Qigang Deng, Ranchao Wu, Hao Wang
wiley +1 more source
A diffusive predator-prey system with prey refuge and gestation delay
Advances in Difference Equations, 2017 The dynamics of a diffusive predator-prey system with prey refuge and gestation delay is investigated in this paper. For a non-delay system, global stability, Turing instability and Hopf bifurcation are studied.
Ruizhi Yang, Haoyu Ren, Xue Cheng
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Forced patterns near a Turing-Hopf bifurcation
, 2009 We study time-periodic forcing of spatially-extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal form analysis yields several predictions, including that (i) weak forcing near the intrinsic Hopf frequency enhances or suppresses
Anne J. Catllá +4 more
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Pattern Formation and Nonlinear Waves Close to a 1:1 Resonant Turing and Turing–Hopf Instability
Studies in Applied Mathematics, Volume 155, Issue 5, November 2025.ABSTRACT In this paper, we analyze the dynamics of a pattern‐forming system close to simultaneous Turing and Turing–Hopf instabilities, which have a 1:1 spatial resonance, that is, they have the same critical wave number. For this, we consider a system of coupled Swift–Hohenberg equations with dispersive terms and general, smooth nonlinearities.
Bastian Hilder, Christian Kuehn
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Boundary Value Problems, 2022 In this paper, a modified cross-diffusion Leslie–Gower predator–prey model with the Beddington–DeAngelis functional response is studied. We use the linear stability analysis on constant steady states to obtain sufficient conditions for the occurrence of ...
Marzieh Farshid, Yaghoub Jalilian
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 12011-12037, August 2025.ABSTRACT In bio‐social models, cooperative behavior has evolved as an adaptive strategy, playing multi‐functional roles. One of such roles in populations is to increase the success of the survival and reproduction of individuals and their families or social groups.
Sangeeta Saha +2 more
wiley +1 more source
Spatiotemporal attractors generated by the Turing-Hopf bifurcation in a time-delayed reaction-diffusion system [PDF]
Discrete & Continuous Dynamical Systems - B, 2017 We study the Turing-Hopf bifurcation and give a simple and explicit calculation formula of the normal forms for a general two-components system of reaction-diffusion equation with time delays. We declare that our formula can be automated by Matlab.
Qi An, Weihua Jiang
semanticscholar +1 more source