Dynamics of a predator–prey system with nonlinear prey-taxis
Changfeng Liu, Shangjiang Guo
Abstract
Abstract In this paper, we investigate a predator–prey system with nonlinear prey-taxis under Neumann boundary condition. For a class of chemotactic sensitive functions, we obtain the existence and boundedness of global classical solutions for initial boundary value problems in arbitrary dimensional space. In addition, we also study the local stability of the constant steady state solution, and obtain the global asymptotic stability of the steady state solution under different predation intensity by constructing appropriate Lyapunov functions. Furthermore, the steady state bifurcation, Hopf bifurcation and fold-Hopf Singularity are analysed in detail by using Lyapunov–Schmidt reduction method.
Topics & Concepts
MathematicsLyapunov functionHopf bifurcationNonlinear systemBifurcationNeumann boundary conditionMathematical analysisExponential stabilityConstant (computer programming)Applied mathematicsBoundary value problemControl theory (sociology)EconomicsComputer scienceControl (management)ManagementQuantum mechanicsProgramming languagePhysicsMathematical Biology Tumor GrowthMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic Dynamics