The aim of this paper is to study the dynamical behaviors of a piecewise smooth predator-prey model with predator harvesting.We consider a harvesting strategy that allows constant catches if the population size is abo...The aim of this paper is to study the dynamical behaviors of a piecewise smooth predator-prey model with predator harvesting.We consider a harvesting strategy that allows constant catches if the population size is above a certain threshold value(to obtain predictable yield)and no catches if the population size is below the threshold(to protect the population).It is shown that boundary equilibrium bifurcation and sliding grazing bifurcation can happen as the threshold value varies.We provide analytical analysis to prove the existence of sliding limit cycles and sliding homoclinic cycles,the coexistence of them with standard limit cycles.Some numerical simulations are given to demonstrate ourresults.展开更多
In this paper,we consider a planar piecewise smooth differential system consisting of a linear system and a quadratic Hamiltonian system.The quadratic system has some folds on the discontinuity line.The linear system ...In this paper,we consider a planar piecewise smooth differential system consisting of a linear system and a quadratic Hamiltonian system.The quadratic system has some folds on the discontinuity line.The linear system may have a focus,saddle or node.Our results show that this piecewise smooth differential system will have two limit cycles and a sliding cycle.Moreover,this piecewise smooth system will undergo pseudo-homoclinic bifurcation,Hopf bifurcation and critical crossing bifurcation CC.Some examples are given to illustrate our results.展开更多
基金This work is supported by NNSFC(No.11871022)Shanghai Key Laboratory of PMMP.
文摘The aim of this paper is to study the dynamical behaviors of a piecewise smooth predator-prey model with predator harvesting.We consider a harvesting strategy that allows constant catches if the population size is above a certain threshold value(to obtain predictable yield)and no catches if the population size is below the threshold(to protect the population).It is shown that boundary equilibrium bifurcation and sliding grazing bifurcation can happen as the threshold value varies.We provide analytical analysis to prove the existence of sliding limit cycles and sliding homoclinic cycles,the coexistence of them with standard limit cycles.Some numerical simulations are given to demonstrate ourresults.
基金partially supported by Postgraduate research and innovation ability cultivation plan of Huaqiao Universitypartially supported by NNSF of China grant11671040+3 种基金Cultivation Program for Outstanding Young Scientific talents of Fujian Province in 2017Program for Innovative Research Team in Science and Technology in Fujian Province UniversityQuanzhou High-Level Talents Support Plan under Grant2017ZT012Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University(ZQN-YX401)
文摘In this paper,we consider a planar piecewise smooth differential system consisting of a linear system and a quadratic Hamiltonian system.The quadratic system has some folds on the discontinuity line.The linear system may have a focus,saddle or node.Our results show that this piecewise smooth differential system will have two limit cycles and a sliding cycle.Moreover,this piecewise smooth system will undergo pseudo-homoclinic bifurcation,Hopf bifurcation and critical crossing bifurcation CC.Some examples are given to illustrate our results.
