This paper investigates the Hopf bifurcation of a 4-dimensional hyperchaotic system withonly one equilibrium.A detailed set of conditions are derived,which guarantee the existence of theHopf bifurcation.Furthermore,th...This paper investigates the Hopf bifurcation of a 4-dimensional hyperchaotic system withonly one equilibrium.A detailed set of conditions are derived,which guarantee the existence of theHopf bifurcation.Furthermore,the standard normal form theory is applied to determine the directionand type of the Hopf bifurcation,and the approximate expressions of bifurcating periodic solutions andtheir periods.In addition,numerical simulations are used to justify theoretical results.展开更多
In this paper,we investigate the stability of the split-step theta(SST)method for a class of nonlinear regime-switching jump systems–neutral stochastic delay differential equations(NSDDEs)with Markov switching and ju...In this paper,we investigate the stability of the split-step theta(SST)method for a class of nonlinear regime-switching jump systems–neutral stochastic delay differential equations(NSDDEs)with Markov switching and jumps.As we know,there are few results on the stability of numerical solutions for NSDDEs with Markov switching and jumps.The purpose of this paper is to enrich conclusions in such respect.It first devotes to show that the trivial solution of the NSDDE with Markov switching and jumps is exponentially mean square stable and asymptotically mean square stable under some suitable conditions.If the drift coefficient also satisfies the linear growth condition,it then proves that the SST method applied to the NSDDE with Markov switching and jumps shares the same conclusions with the exact solution.Moreover,a numerical example is demonstrated to illustrate the obtained results.展开更多
This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov...This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique,and the stochastic ultimate boundedness of this positive solution is also obtained.Sufficient conditions are established for the extinction and persistence of this solution.Moreover,some numerical simulations are carried out to support the obtained results.展开更多
基金supported by National Natural Science Foundation of China(11271139)Guangdong Natural Science Foundation(2014A030313256,S2013040016144)+1 种基金Science and Technology Projects of Guangdong Province(2013B010101009)Tianhe Science and Technology Foundation of Guangzhou(201301YG027)
基金supported by the National Natural Science Foundation of China under Grant Nos. 10871074, 10671105the Natural Science Foundation of Guangdong Province of China under Grant No. 05300162
文摘This paper investigates the Hopf bifurcation of a 4-dimensional hyperchaotic system withonly one equilibrium.A detailed set of conditions are derived,which guarantee the existence of theHopf bifurcation.Furthermore,the standard normal form theory is applied to determine the directionand type of the Hopf bifurcation,and the approximate expressions of bifurcating periodic solutions andtheir periods.In addition,numerical simulations are used to justify theoretical results.
基金This work is partially supported by the National Natural Science Foundation of China(Nos.1190139&11671149,11871225)the Natural Science Foundation of Guangdong Province(No.2017A030312006).
文摘In this paper,we investigate the stability of the split-step theta(SST)method for a class of nonlinear regime-switching jump systems–neutral stochastic delay differential equations(NSDDEs)with Markov switching and jumps.As we know,there are few results on the stability of numerical solutions for NSDDEs with Markov switching and jumps.The purpose of this paper is to enrich conclusions in such respect.It first devotes to show that the trivial solution of the NSDDE with Markov switching and jumps is exponentially mean square stable and asymptotically mean square stable under some suitable conditions.If the drift coefficient also satisfies the linear growth condition,it then proves that the SST method applied to the NSDDE with Markov switching and jumps shares the same conclusions with the exact solution.Moreover,a numerical example is demonstrated to illustrate the obtained results.
基金supported by the National Natural Science Foundation of China(Nos.11901398,11671149,11871225 and 11771102)Guangdong Basic and Applied Basic Research Foundation(No.2019A1515011350)the Fundamental Research Funds for the Central Universities(No.2018MS58).
文摘This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique,and the stochastic ultimate boundedness of this positive solution is also obtained.Sufficient conditions are established for the extinction and persistence of this solution.Moreover,some numerical simulations are carried out to support the obtained results.
