Results 1 to 10 of about 213 (131)
Bifurcations and Turing patterns in a diffusive Gierer–Meinhardt model
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, the Hopf bifurcations and Turing bifurcations of the Gierer–Meinhardt activator-inhibitor model are studied. The very interesting and complex spatially periodic solutions and patterns induced by bifurcations are analyzed from both ...
Yong Wang, Mengping Guo, Weihua Jiang
doaj +3 more sources
Turing instabilities and patterns near a Hopf bifurcation [PDF]
Applied Mathematics and Computation, 2005 27 pages, 5 ...
Rui Dilão
exaly +4 more sources
Turing Instability and Turing–Hopf Bifurcation in Diffusive Schnakenberg Systems with Gene Expression Time Delay [PDF]
Journal of Dynamics and Differential Equations, 2018 For delayed reaction-diffusion Schnakenberg systems with Neumann boundary conditions, critical conditions for Turing instability are derived, which are necessary and sufficient. And existence conditions for Turing, Hopf and Turing-Hopf bifurcations are established.
Weihua Jiang +2 more
exaly +3 more sources
Nonlinear Analysis, 2022 In this paper, we extend a Leslie–Gower-type predator–prey system with ratio-dependent Holling III functional response considering the cost of antipredator defence due to fear.
Hongyu Chen, Chunrui Zhang
doaj +1 more source
On the Proper Treatment of Dynamics in Cognitive Science
Topics in Cognitive Science, EarlyView., 2023 Abstract This essay examines the relevance of dynamical ideas for cognitive science. On its own, the mere mathematical idea of a dynamical system is too weak to serve as a scientific theory of anything, and dynamical approaches within cognitive science are too rich and varied to be subsumed under a single “dynamical hypothesis.” Instead, after first ...
Randall D. Beer
wiley +1 more source
Spatiotemporal dynamics for a diffusive mussel–algae model near a Hopf bifurcation point
Advances in Difference Equations, 2021 In this paper, the Hopf bifurcation and Turing instability for a mussel–algae model are investigated. Through analysis of the corresponding kinetic system, the existence and stability conditions of the equilibrium and the type of Hopf bifurcation are ...
Shihong Zhong, Xuehan Cheng, Biao Liu
doaj +1 more source
IEEE Access, 2021 Great progress has been made in bifurcation control of systems described by ordinary differential equations. However, the control of Hopf bifurcation and Turing patterns is seldom reported in reaction-diffusion systems, which is formed by partial ...
Yunxiang Lu +6 more
doaj +1 more source
The Diffusion-Driven Instability for a General Time-Space Discrete Host-Parasitoid Model
Discrete Dynamics in Nature and Society, 2023 In this paper, we consider a general time-space discrete host-parasitoid model with the periodic boundary conditions. We analyzed and obtained some usual conditions, such as Turing instability occurrence, Flip bifurcation occurrence, and Neimark-Sacker ...
Xuetian Zhang, Chunrui Zhang
doaj +1 more source
Bifurcation and Patterns Analysis for a Spatiotemporal Discrete Gierer-Meinhardt System
Mathematics, 2022 The Gierer-Meinhardt system is one of the prototypical pattern formation models. The bifurcation and pattern dynamics of a spatiotemporal discrete Gierer-Meinhardt system are investigated via the couple map lattice model (CML) method in this paper.
Biao Liu, Ranchao Wu
doaj +1 more source
Entropy, 2023 This paper investigates the complex dynamics of a ratio-dependent predator–prey model incorporating the Allee effect in prey and predator harvesting. To explore the joint effect of the harvesting effort and diffusion on the dynamics of the system, we ...
Meiyao Chen +3 more
doaj +1 more source