Global Exponential Synchronization of Complex-Valued Neural Networks with Time Delays via Matrix Measure Method

In this paper, global exponential synchronization of a class of complex-valued neural networks with time delays is investigated. Based on Halanay inequality theory, Lyapunov theory and matrix measure method, by separating complex-valued neural networks to the real part and imaginary part, several criteria for the global exponentially synchronization of complex-valued neural networks are presented. Finally, one numerical simulation is given to show the effectiveness of our theoretical results.

[1]  Mao Wang,et al.  Synchronization of uncertain chaotic systems with perturbation based on variable structure control , 2006 .

[2]  John H. Mathews,et al.  Complex analysis for mathematics and engineering , 1995 .

[3]  Abdesselem Boulkroune,et al.  Fuzzy generalized projective synchronization of incommensurate fractional-order chaotic systems , 2016, Neurocomputing.

[4]  Jinde Cao,et al.  Generalized synchronization for delayed chaotic neural networks: a novel coupling scheme , 2006 .

[5]  M. Bohner,et al.  Global Stability of Complex-Valued Neural Networks on Time Scales , 2011 .

[6]  Yüksel Özbay,et al.  Fuzzy clustering complex-valued neural network to diagnose cirrhosis disease , 2011, Expert Syst. Appl..

[7]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.

[8]  Zhenjiang Zhao,et al.  Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays , 2016, Neural Networks.

[9]  Jürgen Kurths,et al.  Predicting phase synchronization in a spiking chaotic CO2 laser. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  K. Aihara,et al.  Complex-Valued Multistate Associative Memory With Nonlinear Multilevel Functions for Gray-Level Image Reconstruction , 2009, IEEE Transactions on Neural Networks.

[11]  Guang-Hong Yang,et al.  Adaptive Pinning Control of Deteriorated Nonlinear Coupling Networks With Circuit Realization , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[12]  S. H. Mahboobi,et al.  Observer-based control design for three well-known chaotic systems , 2006 .

[13]  Jamal Daafouz,et al.  Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification , 2005 .

[14]  Jinde Cao,et al.  Matrix measure method for global exponential stability of complex-valued recurrent neural networks with time-varying delays , 2015, Neural Networks.

[15]  Jun Wang,et al.  Global exponential periodicity and stability of discrete-time complex-valued recurrent neural networks with time-delays , 2015, Neural Networks.

[16]  M. Vidyasagar,et al.  Nonlinear systems analysis (2nd ed.) , 1993 .

[17]  Jinde Cao,et al.  Lag Synchronization of Memristor-Based Coupled Neural Networks via $\omega $ -Measure , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Xiaodi Li,et al.  Complete Stability Analysis of Complex-Valued Neural Networks with Time Delays and Impulses , 2014, Neural Processing Letters.

[19]  Zhengwen Tu,et al.  Stability Analysis of Fractional Order Complex-Valued Memristive Neural Networks with Time Delays , 2017, Neural Processing Letters.

[20]  Yicheng Liu,et al.  Local phase synchronization and clustering for the delayed phase-coupled oscillators with plastic coupling , 2016 .

[21]  Xiaodi Li,et al.  Dissipativity analysis of memristor-based complex-valued neural networks with time-varying delays , 2015, Inf. Sci..

[22]  Donal O'Regan,et al.  Global dissipativity of memristor-based complex-valued neural networks with time-varying delays , 2015, Neural Computing and Applications.

[23]  Tohru Nitta,et al.  Orthogonality of Decision Boundaries in Complex-Valued Neural Networks , 2004, Neural Computation.

[24]  Lihong Huang,et al.  Synchronization Criteria for Discontinuous Neural Networks With Mixed Delays via Functional Differential Inclusions , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Akira Hirose,et al.  Recent Progress in Applications of Complex-Valued Neural Networks , 2010, ICAISC.

[26]  Jitao Sun,et al.  Further Investigate the Stability of Complex-Valued Recurrent Neural Networks With Time-Delays , 2014 .

[27]  Hao Zhang,et al.  Synchronization of complex-valued neural network with sliding mode control , 2016, J. Frankl. Inst..

[28]  Yong Li,et al.  Matrix measure strategies for stabilization and synchronization of delayed BAM neural networks , 2016 .

[29]  Lihong Huang,et al.  Periodicity and global exponential stability of generalized Cohen-Grossberg neural networks with discontinuous activations and mixed delays , 2014, Neural Networks.

[30]  Lihong Huang,et al.  New results for global exponential synchronization in neural networks via functional differential inclusions. , 2015, Chaos.

[31]  Zhengqiu Zhang,et al.  Global asymptotic stability for a class of complex-valued Cohen-Grossberg neural networks with time delays , 2016, Neurocomputing.

[32]  Derong Liu TNNLS Call for Reviewers and Special Issues , 2015, IEEE Trans. Neural Networks Learn. Syst..

[33]  Ju H. Park Synchronization of Genesio chaotic system via backstepping approach , 2006 .

[34]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[35]  Akira Hirose,et al.  Complex-Valued Neural Networks , 2006, Studies in Computational Intelligence.

[36]  Binoy Krishna Roy,et al.  Synchronization and anti-synchronization of Lu and Bhalekar–Gejji chaotic systems using nonlinear active control , 2014 .

[37]  Jinde Cao,et al.  Global μ-stability criteria for quaternion-valued neural networks with unbounded time-varying delays , 2016, Inf. Sci..

[38]  Xiaodi Li,et al.  Exponential stability of Cohen-Grossberg-type BAM neural networks with time-varying delays via impulsive control , 2009, Neurocomputing.

[39]  Haibo He,et al.  Editorial IEEE Transactions on Neural Networks and Learning Systems 2016 and Beyond , 2016, IEEE Trans. Neural Networks Learn. Syst..

[40]  Jun Wang,et al.  Global Stability of Complex-Valued Recurrent Neural Networks With Time-Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[41]  Tianping Chen,et al.  Global Exponential Stability for Complex-Valued Recurrent Neural Networks With Asynchronous Time Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[42]  Guodong Zhang,et al.  Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays , 2013, Neural Networks.

[43]  Jinde Cao,et al.  Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays , 2014, Neural Networks.

[44]  Jinde Cao,et al.  Synchronization of fractional-order complex-valued neural networks with time delay , 2016, Neural Networks.

[45]  Akira Hirose,et al.  Complex-Valued Neural Networks: Theories and Applications , 2003 .

[46]  Jianquan Lu,et al.  Global exponential stability for quaternion-valued recurrent neural networks with time-varying delays , 2016, Nonlinear Dynamics.

[47]  Zhenjiang Zhao,et al.  Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects , 2016, Neural Networks.

[48]  Juan Luis García Guirao,et al.  New trends in nonlinear dynamics and chaoticity , 2016 .

[49]  Jinde Cao,et al.  Existence and Uniform Stability Analysis of Fractional-Order Complex-Valued Neural Networks With Time Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[50]  Lihong Huang,et al.  Existence and global asymptotic stability of periodic solution for discrete and distributed time-varying delayed neural networks with discontinuous activations , 2011, Neurocomputing.

[51]  Guanrong Chen,et al.  From Chaos To Order Methodologies, Perspectives and Applications , 1998 .

[52]  Yang Liu,et al.  Global stability of Clifford-valued recurrent neural networks with time delays , 2015, Nonlinear Dynamics.

[53]  Bo Zhou,et al.  Boundedness and complete stability of complex-valued neural networks with time delay. , 2013, IEEE transactions on neural networks and learning systems.

[54]  WangJun,et al.  Global exponential periodicity and stability of discrete-time complex-valued recurrent neural networks with time-delays , 2015 .

[55]  Jinde Cao,et al.  Exponential synchronization of chaotic neural networks: a matrix measure approach , 2009 .

[56]  Zhenjiang Zhao,et al.  Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales , 2016, Neurocomputing.

[57]  Lihong Huang,et al.  Dissipativity and Synchronization of Generalized BAM Neural Networks With Multivariate Discontinuous Activations , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[58]  Qiankun Song,et al.  Stability and Hopf bifurcation analysis of a tri-neuron BAM neural network with distributed delay , 2012, Neurocomputing.

[59]  Chuandong Li,et al.  Complete synchronization of delayed chaotic neural networks by intermittent control with two switches in a control period , 2016, Neurocomputing.

[60]  Dong Xie,et al.  Global exponential stability of periodic solution for delayed complex-valued neural networks with impulses , 2016, Neurocomputing.