In this paper,the existence,uniqueness and global attractivity are discussed on almost periodic solution of SICNNs（shunting inhibitory cellular neural networks）with continuously distributed delays.By using the fixed...In this paper,the existence,uniqueness and global attractivity are discussed on almost periodic solution of SICNNs（shunting inhibitory cellular neural networks）with continuously distributed delays.By using the fixed point theorem,differential inequality technique and Lyapunov functional method,giving the new ranges of parameters,several sufficient conditions are obtained to ensure the existence,uniqueness and global attractivity of almost periodic solution.Compared with the previous studies,our methods are more effective for almost periodic solution analysis of SICNNs with continuously distributed delays.Some existing results have been improved and extended.In order to show the effectiveness of the obtained results,an example is given in this paper.展开更多
By using the Leray-Schauder fixed point theorem,differential inequality techniques and constructing suitable Lyapunov functional,several sufficient conditions are obtained for the existence and global exponential stab...By using the Leray-Schauder fixed point theorem,differential inequality techniques and constructing suitable Lyapunov functional,several sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general shunting inhibitory cellular neural networks with delays.Some new results are obtained and some previously known results are improved.An example is employed to illustrate our feasible results.展开更多
Purpose – The purpose of this paper is to study the existence and exponential stability of anti-periodicsolutions of a class of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays andcontin...Purpose – The purpose of this paper is to study the existence and exponential stability of anti-periodicsolutions of a class of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays andcontinuously distributed delays.Design/methodology/approach – The inequality technique and Lyapunov functional method are applied.Findings – Sufficient conditions are obtained to ensure that all solutions of the networks convergeexponentially to the anti-periodic solution, which are new and complement previously known results.Originality/value – There are few papers that deal with the anti-periodic solutions of delayed SICNNs withthe form negative feedback – aij(t)αij(xij(t)).展开更多
In this paper, a class of two-dimensional shunting inhibitory cellular neural networks with distributed delays and variable coefficients system dxij/dt=-αij（t）xij-∑↑ckl∈Nr（i,j）cij^kl（t）fkl（∫0^＋∞pkl（s）...In this paper, a class of two-dimensional shunting inhibitory cellular neural networks with distributed delays and variable coefficients system dxij/dt=-αij（t）xij-∑↑ckl∈Nr（i,j）cij^kl（t）fkl（∫0^＋∞pkl（s）xkl（t-s）ds）xij＋Lij（t） is studied. By using the Schauder＇s fixed point theorem and Lyapunov function, we obtain some sufficient conditions about the existence and attractivity of almost periodic solutions to the above system, and all its solutions converge to such almost periodic solution. An example is given to illustrate that the conditions of our results are feasible.展开更多
Purpose–The purpose of this paper is to investigate the weighted pseudo-almost periodic solutions of shunting inhibitory cellular neural networks(SICNNs)with time-varying delays and distributed delays.Design/methodol...Purpose–The purpose of this paper is to investigate the weighted pseudo-almost periodic solutions of shunting inhibitory cellular neural networks(SICNNs)with time-varying delays and distributed delays.Design/methodology/approach–The principle of weighted pseudo-almost periodic functions and some new mathematical analysis skills are applied.Findings–A set of sufficient criteria which guarantee the existence and exponential stability of the weighted pseudo-almost periodic solutions of the considered SICNNs are established.Originality/value–The derived results of this paper are new and complement some earlier works.The innovation of this paper concludes two points:a new sufficient criteria guaranteeing the existence and exponential stability of the weighted pseudo-almost periodic solutions of SICNNs are established;and the ideas of this paper can be applied to investigate some other similar neural networks.展开更多
文摘In this paper,the existence,uniqueness and global attractivity are discussed on almost periodic solution of SICNNs（shunting inhibitory cellular neural networks）with continuously distributed delays.By using the fixed point theorem,differential inequality technique and Lyapunov functional method,giving the new ranges of parameters,several sufficient conditions are obtained to ensure the existence,uniqueness and global attractivity of almost periodic solution.Compared with the previous studies,our methods are more effective for almost periodic solution analysis of SICNNs with continuously distributed delays.Some existing results have been improved and extended.In order to show the effectiveness of the obtained results,an example is given in this paper.
基金Supported by the Honghe University Master or Doctor Initial Fund (Grant No.XSS07001)the Scientific Research Fund of Yunnan Provincial Education Department (Grant No.07Y10085)
文摘By using the Leray-Schauder fixed point theorem,differential inequality techniques and constructing suitable Lyapunov functional,several sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general shunting inhibitory cellular neural networks with delays.Some new results are obtained and some previously known results are improved.An example is employed to illustrate our feasible results.
基金This work is supported by National Natural Science Foundation of China(No.61673008 and No.11261010)Project of High-level Innovative Talents of Guizhou Province((2016)5651)Major Research Project of The Innovation Group of The Education Department of Guizhou Province((2017)039).
文摘Purpose – The purpose of this paper is to study the existence and exponential stability of anti-periodicsolutions of a class of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays andcontinuously distributed delays.Design/methodology/approach – The inequality technique and Lyapunov functional method are applied.Findings – Sufficient conditions are obtained to ensure that all solutions of the networks convergeexponentially to the anti-periodic solution, which are new and complement previously known results.Originality/value – There are few papers that deal with the anti-periodic solutions of delayed SICNNs withthe form negative feedback – aij(t)αij(xij(t)).
基金This work was supported by the Foundation of Hunan Provincial Education Department(04C613, 03C009, 05A057).
文摘In this paper, a class of two-dimensional shunting inhibitory cellular neural networks with distributed delays and variable coefficients system dxij/dt=-αij（t）xij-∑↑ckl∈Nr（i,j）cij^kl（t）fkl（∫0^＋∞pkl（s）xkl（t-s）ds）xij＋Lij（t） is studied. By using the Schauder＇s fixed point theorem and Lyapunov function, we obtain some sufficient conditions about the existence and attractivity of almost periodic solutions to the above system, and all its solutions converge to such almost periodic solution. An example is given to illustrate that the conditions of our results are feasible.
基金Supported by Distinguished Expert Science Foundation of Naval Aeronautical and Astronautical University and the Younger Foundation of Yantai University (SX06Z9)
文摘Purpose–The purpose of this paper is to investigate the weighted pseudo-almost periodic solutions of shunting inhibitory cellular neural networks(SICNNs)with time-varying delays and distributed delays.Design/methodology/approach–The principle of weighted pseudo-almost periodic functions and some new mathematical analysis skills are applied.Findings–A set of sufficient criteria which guarantee the existence and exponential stability of the weighted pseudo-almost periodic solutions of the considered SICNNs are established.Originality/value–The derived results of this paper are new and complement some earlier works.The innovation of this paper concludes two points:a new sufficient criteria guaranteeing the existence and exponential stability of the weighted pseudo-almost periodic solutions of SICNNs are established;and the ideas of this paper can be applied to investigate some other similar neural networks.
