In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as...In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.展开更多
The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous ef...The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous efforts that employed separation analysis and the real-valued control design, based on the quaternion-valued signum function and several related properties, a direct analytical method is proposed here and the quaternion-valued controllers are designed in order to discuss the fixed-time synchronization for the relevant quaternion-valued neural networks. In addition, the preassigned-time synchronization is investigated based on a quaternion-valued control design, where the synchronization time is preassigned and the control gains are finite. Compared with existing results, the direct method without separation developed in this article is beneficial in terms of simplifying theoretical analysis, and the proposed quaternion-valued control schemes are simpler and more effective than the traditional design, which adds four real-valued controllers. Finally, two numerical examples are given in order to support the theoretical 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
In this study,we investigate the problem of multiple Mittag-Leffler stability analysis for fractional-order quaternion-valued neural networks(QVNNs)with impulses.Using the geometrical properties of activation function...In this study,we investigate the problem of multiple Mittag-Leffler stability analysis for fractional-order quaternion-valued neural networks(QVNNs)with impulses.Using the geometrical properties of activation functions and the Lipschitz condition,the existence of the equilibrium points is analyzed.In addition,the global Mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order QVNNs is investigated by employing the Lyapunov direct method.Finally,simulation is performed to illustrate the effectiveness and validity of the main results obtained.展开更多
This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed poin...This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks.The results are completely new.Finally,the authors give an example to illustrate the feasibility of the results.展开更多
This paper studies the existence and uniqueness conditions for the quaternion-valued non-linear impulsive system. Firstly, a space of quaternion-valued piecewise functions is constructed and completeness of the space ...This paper studies the existence and uniqueness conditions for the quaternion-valued non-linear impulsive system. Firstly, a space of quaternion-valued piecewise functions is constructed and completeness of the space is also proved. Then by taking advantage of the Bielecki norm and fixed point theorem, existence and uniqueness criteria of quaternion-valued nonlinear impulsive system are obtained. At last, an example is given to illustrate our theoretical results.展开更多
In this paper,cluster synchronization of fractionalorder complex community networks(FOCCNs)in quaternionvalued filed is addressed based on the non-separation approach.To carry out tasks with different requirements,qua...In this paper,cluster synchronization of fractionalorder complex community networks(FOCCNs)in quaternionvalued filed is addressed based on the non-separation approach.To carry out tasks with different requirements,quaternionvalued FOCCNs are divided into several clusters,each of which owns different dynamic behaviors.Considering the interaction of nodes in the cluster and the influence of external driving,a hybrid controller is designed,in which the coupling strength and feedback control gains are simultaneously regulated with the evolution of states.To establish the cluster synchronization criteria for the quaternion-valued FOCCNs,some analytical approaches,such as the mean value theorem and the proof by contradiction are utilized.Furthermore,for the asymptotical synchronization of fractional-order complex networks,the case with identical nodes is also considered as a special case.Finally,two quaternion-valued FOCCNs are divided to synchronize to the desired trajectory,and a numerical simulation shows the validity of the proposed approach.展开更多
An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the pola...An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.展开更多
基金Supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China(201485).
文摘In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.
基金supported by the National Natural Science Foundation of China (61963033, 61866036, 62163035)the Key Project of Natural Science Foundation of Xinjiang (2021D01D10)+1 种基金the Xinjiang Key Laboratory of Applied Mathematics (XJDX1401)the Special Project for Local Science and Technology Development Guided by the Central Government (ZYYD2022A05)。
文摘The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous efforts that employed separation analysis and the real-valued control design, based on the quaternion-valued signum function and several related properties, a direct analytical method is proposed here and the quaternion-valued controllers are designed in order to discuss the fixed-time synchronization for the relevant quaternion-valued neural networks. In addition, the preassigned-time synchronization is investigated based on a quaternion-valued control design, where the synchronization time is preassigned and the control gains are finite. Compared with existing results, the direct method without separation developed in this article is beneficial in terms of simplifying theoretical analysis, and the proposed quaternion-valued control schemes are simpler and more effective than the traditional design, which adds four real-valued controllers. Finally, two numerical examples are given in order to support the theoretical 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In this study,we investigate the problem of multiple Mittag-Leffler stability analysis for fractional-order quaternion-valued neural networks(QVNNs)with impulses.Using the geometrical properties of activation functions and the Lipschitz condition,the existence of the equilibrium points is analyzed.In addition,the global Mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order QVNNs is investigated by employing the Lyapunov direct method.Finally,simulation is performed to illustrate the effectiveness and validity of the main results obtained.
基金supported by the National Natural Sciences Foundation of People’s Republic of China under Grants Nos.11861072 and 11361072.
文摘This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks.The results are completely new.Finally,the authors give an example to illustrate the feasibility of the results.
基金supported by the National Natural Science Foundation of China under Grant No.61673296
文摘This paper studies the existence and uniqueness conditions for the quaternion-valued non-linear impulsive system. Firstly, a space of quaternion-valued piecewise functions is constructed and completeness of the space is also proved. Then by taking advantage of the Bielecki norm and fixed point theorem, existence and uniqueness criteria of quaternion-valued nonlinear impulsive system are obtained. At last, an example is given to illustrate our theoretical results.
基金supported by the National Natural Science Foundation of China(No.62373089)the Synthetical Automation for Process Industries(SAPI)Fundamental Research Funds(No.2018ZCX22)the Natural Science Foundation of Liaoning Province,China(No.2022JH25/10100008).
文摘In this paper,cluster synchronization of fractionalorder complex community networks(FOCCNs)in quaternionvalued filed is addressed based on the non-separation approach.To carry out tasks with different requirements,quaternionvalued FOCCNs are divided into several clusters,each of which owns different dynamic behaviors.Considering the interaction of nodes in the cluster and the influence of external driving,a hybrid controller is designed,in which the coupling strength and feedback control gains are simultaneously regulated with the evolution of states.To establish the cluster synchronization criteria for the quaternion-valued FOCCNs,some analytical approaches,such as the mean value theorem and the proof by contradiction are utilized.Furthermore,for the asymptotical synchronization of fractional-order complex networks,the case with identical nodes is also considered as a special case.Finally,two quaternion-valued FOCCNs are divided to synchronize to the desired trajectory,and a numerical simulation shows the validity of the proposed approach.
基金supported by Startup Foundation for Phd Research of Henan Normal University(No.5101119170155).
文摘An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.
