Theorems of iteration g-contractive sequential composite mapping and periodic mapping in Banach or probabilistic Bannach space are proved, which allow some contraction ratios of the sequence of mapping might be larger...Theorems of iteration g-contractive sequential composite mapping and periodic mapping in Banach or probabilistic Bannach space are proved, which allow some contraction ratios of the sequence of mapping might be larger than or equal to 1, and are more general than the Banach contraction mapping theorem. Application to the proof of existence of solutions of cycling coupled nonlinear differential equations arising from prey-predator system and A&H stock prices are given.展开更多
The principle aim of this paper is to explore the existence of periodic solution of neural networks model with neutral delay. Sufficient and realistic conditions are obtained by means of an abstract continuous theorem...The principle aim of this paper is to explore the existence of periodic solution of neural networks model with neutral delay. Sufficient and realistic conditions are obtained by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.展开更多
This paper considers a dynamical system defined by a set of ordinary autonomous differential equations with discontinuous right-hand side. Such systems typically appear in economic modelling where there are two or mor...This paper considers a dynamical system defined by a set of ordinary autonomous differential equations with discontinuous right-hand side. Such systems typically appear in economic modelling where there are two or more regimes with a switching between them. Switching between regimes may be a consequence of market forces or deliberately forced in form of policy implementation. Stiefenhofer and Giesl [1] introduce such a model. The purpose of this paper is to show that a metric function defined between two adjacent trajectories contracts in forward time leading to exponentially asymptotically stability of (non)smooth periodic orbits. Hence, we define a local contraction function and distribute it over the smooth and nonsmooth parts of the periodic orbits. The paper shows exponentially asymptotical stability of a periodic orbit using a contraction property of the distance function between two adjacent nonsmooth trajectories over the entire periodic orbit. Moreover it is shown that the ω-limit set of the (non)smooth periodic orbit for two adjacent initial conditions is the same.展开更多
In this paper, by using the contraction mapping principle and constructing a suitable Lyapunov functional, we established a set of easily applicable criteria for the existence, uniqueness and global attractivity of po...In this paper, by using the contraction mapping principle and constructing a suitable Lyapunov functional, we established a set of easily applicable criteria for the existence, uniqueness and global attractivity of positive periodic solution and positive almost periodic solution of a neutral multi-species Logarithmic population model with multiple delays and impulses. The results improve and generalize the known ones in [1], as an application, we also give an example to illustrate the feasibility of our main results.展开更多
文摘Theorems of iteration g-contractive sequential composite mapping and periodic mapping in Banach or probabilistic Bannach space are proved, which allow some contraction ratios of the sequence of mapping might be larger than or equal to 1, and are more general than the Banach contraction mapping theorem. Application to the proof of existence of solutions of cycling coupled nonlinear differential equations arising from prey-predator system and A&H stock prices are given.
文摘The principle aim of this paper is to explore the existence of periodic solution of neural networks model with neutral delay. Sufficient and realistic conditions are obtained by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.
文摘This paper considers a dynamical system defined by a set of ordinary autonomous differential equations with discontinuous right-hand side. Such systems typically appear in economic modelling where there are two or more regimes with a switching between them. Switching between regimes may be a consequence of market forces or deliberately forced in form of policy implementation. Stiefenhofer and Giesl [1] introduce such a model. The purpose of this paper is to show that a metric function defined between two adjacent trajectories contracts in forward time leading to exponentially asymptotically stability of (non)smooth periodic orbits. Hence, we define a local contraction function and distribute it over the smooth and nonsmooth parts of the periodic orbits. The paper shows exponentially asymptotical stability of a periodic orbit using a contraction property of the distance function between two adjacent nonsmooth trajectories over the entire periodic orbit. Moreover it is shown that the ω-limit set of the (non)smooth periodic orbit for two adjacent initial conditions is the same.
文摘In this paper, by using the contraction mapping principle and constructing a suitable Lyapunov functional, we established a set of easily applicable criteria for the existence, uniqueness and global attractivity of positive periodic solution and positive almost periodic solution of a neutral multi-species Logarithmic population model with multiple delays and impulses. The results improve and generalize the known ones in [1], as an application, we also give an example to illustrate the feasibility of our main results.
