Pursuit-evasion wave trains in prey-predator systems with diffusionally coupled delays

DOI10.1007/BF02461065zbMath0446.92018OpenAlexW4253011437MaRDI QIDQ1146138

Kondalsamy Gopalsamy

Publication date: 1980

Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02461065

zbMATH Keywords

Hopf bifurcationLyapunov functionalexistence of periodic solutionsequilibrium solutiontravelling wave solutionLotka-Volterra system of prey-predator equationspursuit-evasion wave trains

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Population dynamics (general) (92D25) Stability theory for integral equations (45M10)

Related Items (7)

Hopf bifurcation analysis in a diffusive food-chain model with time delay ⋮ The Hopf bifurcation and stability of delayed predator-prey system ⋮ Stability analysis and finite volume element discretization for delay-driven spatio-temporal patterns in a predator-prey model ⋮ Instability in diffusive ecolocical models with nonlocal delay effects ⋮ A remark on \(L^{\infty}\) bounds for solutions to quasilinear reaction- diffusion equations ⋮ Well-posedness of abstract integro-differential equations with state-dependent delay ⋮ Pattern dynamics in a diffusive Rössler model

Cites Work

• Unnamed Item
• Time delay in prey-predator models
• On the behavior of solutions of predator-prey equations with hereditary terms
• Spatial structures in predator-prey communities - a nonlinear time delay diffusional model
• Periodic and traveling wave solutions to Volterra-Lotka equations with diffusion
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Time delay in prey-predator models. II: Bifurcation theory
• Bifurcation analysis of nonlinear reaction diffusion equations I. Evolution equations and the steady state solutions
• Nonlinear reaction-diffusion models for interacting populations
• Three types of matrix stability
• Bifurcation of periodic oscillations due to delays in single species growth models
• Topics in stability and bifurcation theory

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