In this paper,three competitive systems with different kinds of state-dependent control are presented and investigated.The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems tha...In this paper,three competitive systems with different kinds of state-dependent control are presented and investigated.The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems that incorporate just one kind of state-dependent control is obtained by applying differential equation geometry theory,and the stability of the order-1 periodic solution of each system is also given.Besides,sufficient conditions for the existence and stability of the order-2 periodic solution of the system that incorporate two kinds of state-dependent control are gained by successor function method and analogue of Poincare criterion,respectively.Finally,numerical simulations are carried out to verify the theoretical results.展开更多
In this paper,the system with impulsive state feedback control corresponding to the sulphitation reaction in process of manufacturo of sugar is considered.By means of square approximation and a series of switched syst...In this paper,the system with impulsive state feedback control corresponding to the sulphitation reaction in process of manufacturo of sugar is considered.By means of square approximation and a series of switched systems,the periodic solution is approximated by a series of continuous hybrid limit cycles.Similar to the analysis of limit cycles of continuous systems,the existence and stability criteria of the order-1 periodic solution are obtained.Further,numerical analysis and discussion are given.展开更多
The price fluctuation of commodities affects their demand,and it strongly influences the development of industry and the stability of the international economy.A price-output model with two price-dependent impulses is...The price fluctuation of commodities affects their demand,and it strongly influences the development of industry and the stability of the international economy.A price-output model with two price-dependent impulses is presented in this paper to describe their mutual restrictions and the price adjustment strategies.The equilibria and dynamic properties of the impulsive-free price-output model are qualitatively analyzed,and the results show the hazard of free price fluctuation.For the price-output model with two price-dependent impulses,conditions for the existence of the order-2 periodic solution are obtained,and the orbital asymptotic stability is proved.Those results reveal the positive role of price adjustment strategies.Finally,some numerical simulations are carried out to verify the theoretical results.展开更多
基金The authors would like to thank the anonymous referees and Professor Lansun Chen for their very valuable comments,which led to a significant improveinent of the original paper.This work is supposed by the National Natural Science Foundation of China(No.11671346)Nanhu Scholars Program of XYNU.
文摘In this paper,three competitive systems with different kinds of state-dependent control are presented and investigated.The existence of the order-1 homoclinic orbit and order-1 periodic solution of the two systems that incorporate just one kind of state-dependent control is obtained by applying differential equation geometry theory,and the stability of the order-1 periodic solution of each system is also given.Besides,sufficient conditions for the existence and stability of the order-2 periodic solution of the system that incorporate two kinds of state-dependent control are gained by successor function method and analogue of Poincare criterion,respectively.Finally,numerical simulations are carried out to verify the theoretical results.
基金This work is supported by the National Natural Science Foundation of China(61751317)the Natural Science Foundation of Guangxi Province(2018JJA110058,2019JJA110027)the Scientific Research Fund of Yulin Normal University for High-level Talents(G2019ZK18).
文摘In this paper,the system with impulsive state feedback control corresponding to the sulphitation reaction in process of manufacturo of sugar is considered.By means of square approximation and a series of switched systems,the periodic solution is approximated by a series of continuous hybrid limit cycles.Similar to the analysis of limit cycles of continuous systems,the existence and stability criteria of the order-1 periodic solution are obtained.Further,numerical analysis and discussion are given.
基金This work is supported by the National Natural Science Foundation of China(No.11701026,No.12071407)the Fundaineiital Researcli Funds of Beijing University of Civil Engineering and Architecture(No.X18225,No.XI9031)the Post Graduate Innovation Project of Beijing University of Civil Engineering and Architecture(No.PG2020098).
文摘The price fluctuation of commodities affects their demand,and it strongly influences the development of industry and the stability of the international economy.A price-output model with two price-dependent impulses is presented in this paper to describe their mutual restrictions and the price adjustment strategies.The equilibria and dynamic properties of the impulsive-free price-output model are qualitatively analyzed,and the results show the hazard of free price fluctuation.For the price-output model with two price-dependent impulses,conditions for the existence of the order-2 periodic solution are obtained,and the orbital asymptotic stability is proved.Those results reveal the positive role of price adjustment strategies.Finally,some numerical simulations are carried out to verify the theoretical results.
