This paper investigates the polynomial synchronization(PS)problem of complex-valued inertial neural networks with multi-proportional delays.It is analyzed based on the non-separation method.Firstly,an exponential tran...This paper investigates the polynomial synchronization(PS)problem of complex-valued inertial neural networks with multi-proportional delays.It is analyzed based on the non-separation method.Firstly,an exponential transformation is applied and an appropriate controller is designed.Then,a new sufficient criterion for PS of the considered system is derived by the Lyapunov function approach and some inequalities techniques.In the end,a numerical example is given to illustrate the effectiveness of the obtained result.展开更多
This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed delays(mixed delays). First, by constructing a proper variable substi...This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed delays(mixed delays). First, by constructing a proper variable substitution, the original inertial neural networks can be rewritten as a first-order differential system. Second, by constructing Lyapunov functions and using differential inequalities,some new and effective criteria are obtained for ensuring the finite-time synchronization. Finally, three numerical examples are also given at the end of this paper to show the effectiveness of the results.展开更多
Periodicity, anti-periodicity and almost periodicity are significant dynamic behaviors of time-varying neural networks. This paper researches the dynamics of anti-periodic solutions for a kind of inertial Quaternion-v...Periodicity, anti-periodicity and almost periodicity are significant dynamic behaviors of time-varying neural networks. This paper researches the dynamics of anti-periodic solutions for a kind of inertial Quaternion-valued Hopfield neural networks with varying-time delays.Without resolving the explored neural networks into real-valued systems, in the light of a continuation theorem of coincidence degree theory and inequality skills, by constructing different Lyapunov functions from those constructed in the existing research of the stability of equilibrium point, periodic solutions and anti-periodic solutions for neural networks, a newfangled sufficient condition insuring the existence of periodic solutions for above neural networks is gained. By constructing the same Lyapunov functions as those constructed in the proof of the existence of anti-periodic solutions, the newfangled asymptotic stability of anti-periodic solutions for above networks is acquired.展开更多
This paper is concerned with inertial bidirectional associative memory neural networks with mixed delays and impulsive effects.New and practical conditions are given to study the existence,uniqueness,and global expone...This paper is concerned with inertial bidirectional associative memory neural networks with mixed delays and impulsive effects.New and practical conditions are given to study the existence,uniqueness,and global exponential stability of anti-periodic solutions for the suggested system.We use differential inequality techniques to prove our main results.Finally,we give an illustrative example to demonstrate the effectiveness of our new results.展开更多
This present work uses different methods to synchronize the inertial memristor systems with linear coupling. Firstly, the mathematical model of inertial memristor-based neural networks(IMNNs) with time delay is propos...This present work uses different methods to synchronize the inertial memristor systems with linear coupling. Firstly, the mathematical model of inertial memristor-based neural networks(IMNNs) with time delay is proposed, where the coupling matrix satisfies the diffusion condition, which can be symmetric or asymmetric. Secondly, by using differential inclusion method and Halanay inequality, some algebraic self-synchronization criteria are obtained. Then, via constructing effective Lyapunov functional, designing discontinuous control algorithms, some new sufficient conditions are gained to achieve synchronization of networks. Finally, two illustrative simulations are provided to show the validity of the obtained results, which cannot be contained by each other.展开更多
This paper presents an Euler discretized inertial delayed neuron model, and its bifurcation dynamical behaviors are discussed. By using the associated characteristic model, center manifold theorem and the normal form ...This paper presents an Euler discretized inertial delayed neuron model, and its bifurcation dynamical behaviors are discussed. By using the associated characteristic model, center manifold theorem and the normal form method, it is shown that the model not only undergoes codimension one(flip, Neimark-Sacker) bifurcation, but also undergoes cusp and resonance bifurcation(1:1 and 1:2) of codimension two. Further, it is found that the parity of delay has some effect on bifurcation behaviors. Finally, some numerical simulations are given to support the analytic results and explore complex dynamics, such as periodic orbits near homoclinic orbits, quasiperiodic orbits, and chaotic orbits.展开更多
基金the National Natural Science Foundation of China (61503222, 62173214)the Natural Science Foundation of Shandong Province of China (ZR2021MF100)+2 种基金the Research Fund for the Taishan Scholar Project of Shandong Province of Chinain part by the Science and Technology Support Plan for Youth Innovation of Colleges and Universities of Shandong Province of China (2019KJI005)in part by the SDUST Research Fund
文摘This paper investigates the polynomial synchronization(PS)problem of complex-valued inertial neural networks with multi-proportional delays.It is analyzed based on the non-separation method.Firstly,an exponential transformation is applied and an appropriate controller is designed.Then,a new sufficient criterion for PS of the considered system is derived by the Lyapunov function approach and some inequalities techniques.In the end,a numerical example is given to illustrate the effectiveness of the obtained result.
文摘This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed delays(mixed delays). First, by constructing a proper variable substitution, the original inertial neural networks can be rewritten as a first-order differential system. Second, by constructing Lyapunov functions and using differential inequalities,some new and effective criteria are obtained for ensuring the finite-time synchronization. Finally, three numerical examples are also given at the end of this paper to show the effectiveness of the results.
基金Supported by the Basic Research Expenses for Provincial Colleges and Universities(Grant No.JYT2020030)。
文摘Periodicity, anti-periodicity and almost periodicity are significant dynamic behaviors of time-varying neural networks. This paper researches the dynamics of anti-periodic solutions for a kind of inertial Quaternion-valued Hopfield neural networks with varying-time delays.Without resolving the explored neural networks into real-valued systems, in the light of a continuation theorem of coincidence degree theory and inequality skills, by constructing different Lyapunov functions from those constructed in the existing research of the stability of equilibrium point, periodic solutions and anti-periodic solutions for neural networks, a newfangled sufficient condition insuring the existence of periodic solutions for above neural networks is gained. By constructing the same Lyapunov functions as those constructed in the proof of the existence of anti-periodic solutions, the newfangled asymptotic stability of anti-periodic solutions for above networks is acquired.
文摘This paper is concerned with inertial bidirectional associative memory neural networks with mixed delays and impulsive effects.New and practical conditions are given to study the existence,uniqueness,and global exponential stability of anti-periodic solutions for the suggested system.We use differential inequality techniques to prove our main results.Finally,we give an illustrative example to demonstrate the effectiveness of our new results.
基金supported by the National Natural Science Foundation of China(Grant Nos.61573096,61374079 and 61603125)the Chinese Scholarship Council(Grent No.201708410029)+1 种基金the"333 Engineering"Foundation of Jiangsu Province of China(Grant No.BRA2015286)Key Program of Henan Universities(Grant No.17A120001)
文摘This present work uses different methods to synchronize the inertial memristor systems with linear coupling. Firstly, the mathematical model of inertial memristor-based neural networks(IMNNs) with time delay is proposed, where the coupling matrix satisfies the diffusion condition, which can be symmetric or asymmetric. Secondly, by using differential inclusion method and Halanay inequality, some algebraic self-synchronization criteria are obtained. Then, via constructing effective Lyapunov functional, designing discontinuous control algorithms, some new sufficient conditions are gained to achieve synchronization of networks. Finally, two illustrative simulations are provided to show the validity of the obtained results, which cannot be contained by each other.
基金supported by the National Priorities Research Program through the Qatar National Research Funda member of Qatar Foundation(Grant No.NPRP 4-1162-1-181)+2 种基金the Natural Science Foundation of China(Grant Nos.6140331361374078&61375102)the Natural Science Foundation Project of Chongqing CSTC(Grant No.cstc2014jcyj A40014)
文摘This paper presents an Euler discretized inertial delayed neuron model, and its bifurcation dynamical behaviors are discussed. By using the associated characteristic model, center manifold theorem and the normal form method, it is shown that the model not only undergoes codimension one(flip, Neimark-Sacker) bifurcation, but also undergoes cusp and resonance bifurcation(1:1 and 1:2) of codimension two. Further, it is found that the parity of delay has some effect on bifurcation behaviors. Finally, some numerical simulations are given to support the analytic results and explore complex dynamics, such as periodic orbits near homoclinic orbits, quasiperiodic orbits, and chaotic orbits.
