Input-to-State Stability for Impulsive Gilpin-Ayala Competition Model With Reaction Diffusion and Delayed Feedback
Ruofeng Rao, Quanxin Zhu, Kaibo Shi
Abstract
This study focuses on the input-to-state stability issue for impulsive Gilpin-Ayala competition model with reaction diffusion and delayed feedback. By using a fixed point theorem, variational method and Lyapunov function method, the unique existence of globally asymptotical input-to-state stability of positive stationary solution is established under Dirichlet zero boundary value. Remarkably, it is the first paper to derive the unique existence of the stationary solution of Reaction-Diffusion (RD) Gilpin-Ayala competition model, which is globally asymptotical input-to-state stability. In the end, simulation results are presented to validate the effectiveness and feasibility of the proposed results.
Topics & Concepts
Stability (learning theory)MathematicsReaction–diffusion systemDiffusionLyapunov functionState (computer science)Control theory (sociology)Competition (biology)Applied mathematicsDirichlet distributionFixed-point theoremFixed pointBoundary value problemComputer scienceMathematical analysisControl (management)Nonlinear systemAlgorithmPhysicsEcologyMachine learningArtificial intelligenceThermodynamicsBiologyQuantum mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsNeural Networks Stability and Synchronizationstochastic dynamics and bifurcation