Synchronization and periodicity of coupled inertial memristive neural networks with supremums

This paper investigates the periodicity and synchronization of inertial memristive neural networks with supremums and time delays. The analysis in this paper employs the results from the theory of differential equations with discontinuous right-hand side as introduced by Filippov. Further, by employing the second order differential inclusion theory and then choosing suitable variable transformation, the original system can be transformed into first order differential equations. By using the matrix measure method and Halany inequality techniques, the sufficient condition that guarantee the global exponential synchronization of drive-response system of coupled inertial memristive neural networks via the state feedback controller is derived. Furthermore, the global exponential periodicity of the addressed neural networks is also discussed. Finally, numerical examples and simulations are given to demonstrate the validation of the proposed results.

[1]  Guanrong Chen,et al.  Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling , 2010 .

[2]  Yang Tang,et al.  Stability analysis of switched stochastic neural networks with time-varying delays , 2014, Neural Networks.

[3]  Lihong Huang,et al.  Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays , 2014, Commun. Nonlinear Sci. Numer. Simul..

[4]  Z. Duan,et al.  Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Guanrong Chen,et al.  Synchronization transitions on small-world neuronal networks: Effects of information transmission delay and rewiring probability , 2008 .

[6]  Jinde Cao,et al.  Exponential stability and periodic oscillatory solution in BAM networks with delays , 2002, IEEE Trans. Neural Networks.

[7]  Huijun Gao,et al.  Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses , 2015, Autom..

[8]  Ivanka M. Stamova,et al.  Lyapunov–Razumikhin method for impulsive differential equations with ‘supremum’ , 2011 .

[9]  Jinde Cao,et al.  Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach , 2014, Neural Networks.

[10]  Jinde Cao,et al.  Pinning synchronization of coupled inertial delayed neural networks , 2014, Cognitive Neurodynamics.

[11]  J. Kurths,et al.  Spatial coherence resonance on diffusive and small-world networks of Hodgkin-Huxley neurons. , 2008, Chaos.

[12]  Yang Tang,et al.  Exponential Synchronization of Coupled Switched Neural Networks With Mode-Dependent Impulsive Effects , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[13]  M. Perc,et al.  Complex synchronous behavior in interneuronal networks with delayed inhibitory and fast electrical synapses. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Huaguang Zhang,et al.  Synchronization analysis for static neural networks with hybrid couplings and time delays , 2015, Neurocomputing.

[15]  Peng Wang,et al.  Global exponential stability of almost periodic solution of delayed neural networks with discontinuous activations , 2013, Inf. Sci..

[16]  Zhigang Zeng,et al.  Almost periodic solutions for a memristor-based neural networks with leakage, time-varying and distributed delays , 2015, Neural Networks.

[17]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[18]  Leimin Wang,et al.  Design of controller on synchronization of memristor-based neural networks with time-varying delays , 2015, Neurocomputing.

[19]  Runhe Qiu,et al.  Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays☆ , 2008 .

[20]  Jinde Cao,et al.  Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers , 2015, J. Frankl. Inst..

[21]  Jinde Cao,et al.  Finite-time synchronization of coupled networks with one single time-varying delay coupling , 2015, Neurocomputing.

[22]  Li Yang,et al.  Existence and exponential stability of periodic solution for stochastic Hopfield neural networks on time scales , 2015, Neurocomputing.

[23]  Guanrong Chen,et al.  Synchronous Bursts on Scale-Free Neuronal Networks with Attractive and Repulsive Coupling , 2010, PloS one.

[24]  Juan J. Nieto,et al.  The Method of Upper and Lower Solutions for Second Order Differential Inclusions with Integral Boundary Conditions , 2010 .

[25]  J. Tour,et al.  Electronics: The fourth element , 2008, Nature.

[26]  Jinde Cao,et al.  Adaptive synchronization of uncertain dynamical networks with delayed coupling , 2008 .

[27]  Quan Yin,et al.  Global exponential periodicity and stability of a class of memristor-based recurrent neural networks with multiple delays , 2013, Inf. Sci..

[28]  Austin Blaquière,et al.  Nonlinear System Analysis , 1966 .

[29]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[30]  Daniel W. C. Ho,et al.  Globally Exponential Synchronization and Synchronizability for General Dynamical Networks , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[31]  Matjaž Perc,et al.  Effects of small-world connectivity on noise-induced temporal and spatial order in neural media , 2007 .

[32]  X. Liao,et al.  Dynamics of an inertial two-neuron system with time delay , 2009 .

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

[34]  Zhigang Zeng,et al.  Global exponential synchronization of memristor-based recurrent neural networks with time-varying delays , 2013, Neural Networks.

[35]  Z. Duan,et al.  Delay-enhanced coherence of spiral waves in noisy Hodgkin–Huxley neuronal networks , 2008 .

[36]  Fernando Corinto,et al.  Nonlinear Dynamics of Memristor Oscillators , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[37]  Zhigang Zeng,et al.  On the periodic dynamics of memristor-based neural networks with time-varying delays , 2014, Inf. Sci..

[38]  Jinde Cao,et al.  Periodicity and synchronization of coupled memristive neural networks with supremums , 2015, Neurocomputing.

[39]  L. Chua.  Memristor-The missing circuit element , 1971 .

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

[41]  Wei Zhang,et al.  Exponential stability of inertial BAM neural networks with time-varying delay via periodically intermittent control , 2015, Neural Computing and Applications.

[42]  Zhigang Zeng,et al.  Global exponential almost periodicity of a delayed memristor-based neural networks , 2014, Neural Networks.

[43]  Bo Liu,et al.  Generalized Halanay Inequalities and Their Applications to Neural Networks With Unbounded Time-Varying Delays , 2011, IEEE Transactions on Neural Networks.

[44]  Lihong Huang,et al.  Periodic synchronization in delayed memristive neural networks based on Filippov systems , 2015, J. Frankl. Inst..

[45]  Xiaodi Li,et al.  Global exponential stability of a class of impulsive cellular neural networks with supremums , 2014 .

[46]  X. Liao,et al.  Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation , 2009 .

[47]  Jinde Cao,et al.  An estimation of the domain of attraction and convergence rate for Hopfield continuous feedback neural networks , 2004 .