Hopf bifurcation and stability of a competition diffusion system with distributed delay

DOI10.2977/prims/1145475224zbMath1086.92056OpenAlexW1986600971MaRDI QIDQ2580240

Li Zhou, Yanbin Tang

Publication date: 18 January 2006

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1145475224

zbMATH Keywords

Hopf bifurcationdistributed delayspatiotemporal structurecompetition diffusionspatially homogeneous periodic solutioncenter-manifold computation

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Partial functional-differential equations (35R10) Ecology (92D40) Bifurcations in context of PDEs (35B32)

Related Items (12)

Bifurcation in a reaction-diffusion model with nonlocal delay effect and nonlinear boundary condition ⋮ Global dynamics and complex patterns in Lotka-Volterra systems: the effects of both local and nonlocal intraspecific and interspecific competitions ⋮ Hopf bifurcation in a reaction-diffusion-advection two species model with nonlocal delay effect ⋮ Spatially nonhomogeneous equilibrium in a reaction-diffusion system with distributed delay ⋮ Bifurcation and stability of a Mimura-Tsujikawa model with nonlocal delay effect ⋮ Patterns in a nonlocal time-delayed reaction-diffusion equation ⋮ Stability switch and Hopf bifurcation for a diffusive prey-predator system with delay ⋮ Multiple spatiotemporal coexistence states and Turing-Hopf bifurcation in a Lotka-Volterra competition system with nonlocal delays ⋮ Stability and Hopf bifurcation analysis in a Lotka–Volterra competition–diffusion–advection model with time delay effect ^* ⋮ Bifurcation analysis on a reactor model with combination of quadratic and cubic steps ⋮ Oscillatory and Stationary Patterns in a Diffusive Model with Delay Effect ⋮ Stability and bifurcation in a reaction-diffusion model with nonlocal delay effect

Cites Work

• Oscillations in a system with material cycling
• Semigroups of linear operators and applications to partial differential equations
• Multiple limit cycles in predator-prey models
• On bifurcations and chaos in predator-prey models with delay
• Theory of functional differential equations. 2nd ed
• Parameter domains for instability of uniform states in systems with many delays
• Stability and Hopf bifurcation for a delay competition diffusion system.
• Theory and applications of partial functional differential equations
• Asymptotic behavior of a competition—diffusion system in population dynamics
• Turing Instability in Competition Models with Delay I: Linear Theory
• Analysis of Spatial Structure in a Predator-Prey Model with Delay II: Nonlinear Theory
• Stability and Traveling Fronts in Lotka-Volterra Competition Models with Stage Structure
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