Stability and bifurcation analysis of an amensalism system with Allee effect
Ming Zhao, Yunfei Du
Abstract
Abstract In this work, we propose and study a new amensalism system with Allee effect on the first species. First, we investigate the existence and stability of all possible coexistence equilibrium points and boundary equilibrium points of this system. Then, applying the Sotomayor theorem, we prove that there exists a saddle-node bifurcation under some suitable parameter conditions. Finally, we provide a specific example with corresponding numerical simulations to further demonstrate our theoretical results.
Topics & Concepts
Allee effectMathematicsOrdinary differential equationBifurcationStability (learning theory)Applied mathematicsSaddle-node bifurcationWork (physics)Partial differential equationSaddle pointEquilibrium pointBoundary (topology)Mathematical analysisDifferential equationNonlinear systemGeometryComputer sciencePhysicsThermodynamicsDemographyPopulationQuantum mechanicsSociologyMachine learningMathematical and Theoretical Epidemiology and Ecology ModelsAdvanced Differential Equations and Dynamical SystemsNonlinear Dynamics and Pattern Formation