Novel results on projective synchronization of fractional-order neural networks with multiple time delays

Abstract This paper investigates a projective synchronization of fractional-order neural networks (FONN) with multiple time delays, and two new synchronization conditions are derived by combining open loop control and linear control. This is achieved by employing stability theorem of linear fractional order systems with multiple delays and comparison principle. Feasibility of the theoretical results is validated through numerical simulations.

[1]  Jinde Cao,et al.  Synchronization of a class of fractional-order neural networks with multiple time delays by comparison principles , 2017, Nonlinear Analysis: Modelling and Control.

[2]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[3]  Zhigang Zeng,et al.  Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks , 2014, Neural Networks.

[4]  N. Laskin Fractional quantum mechanics and Lévy path integrals , 1999, hep-ph/9910419.

[5]  Haipeng Peng,et al.  Finite-time generalized projective lag synchronization criteria for neutral-type neural networks with delay , 2018 .

[6]  Jinde Cao,et al.  Bifurcations in a delayed fractional complex-valued neural network , 2017, Appl. Math. Comput..

[7]  Jinde Cao,et al.  Stability and synchronization of memristor-based fractional-order delayed neural networks , 2015, Neural Networks.

[8]  Haijun Jiang,et al.  Α-stability and Α-synchronization for Fractional-order Neural Networks , 2012, Neural Networks.

[9]  Manuel A. Duarte-Mermoud,et al.  Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems , 2015, Commun. Nonlinear Sci. Numer. Simul..

[10]  Jinde Cao,et al.  Stability and synchronization of fractional-order memristive neural networks with multiple delays , 2017, Neural Networks.

[11]  Jinde Cao,et al.  Projective synchronization of fractional-order memristor-based neural networks , 2015, Neural Networks.

[12]  R. Hilfer Applications Of Fractional Calculus In Physics , 2000 .

[13]  Hu Wang,et al.  Synchronization for fractional-order time-delayed memristor-based neural networks with parameter uncertainty , 2016, J. Frankl. Inst..

[14]  R. Rakkiyappan,et al.  Hybrid projective synchronization of fractional-order memristor-based neural networks with time delays , 2015, Nonlinear Dynamics.

[15]  Jinde Cao,et al.  Synchronization in Fractional-Order Complex-Valued Delayed Neural Networks , 2018, Entropy.

[16]  Lili Zhang,et al.  Generalized matrix projective outer synchronization of non-dissipatively coupled time-varying complex dynamical networks with nonlinear coupling functions , 2017, Neurocomputing.

[17]  Jinde Cao,et al.  Adaptive synchronization of fractional-order memristor-based neural networks with time delay , 2015, Nonlinear Dynamics.

[18]  Haijun Jiang,et al.  Projective synchronization for fractional neural networks , 2014, Neural Networks.

[19]  Jinde Cao,et al.  Fixed-time synchronization of delayed memristor-based recurrent neural networks , 2017, Science China Information Sciences.

[20]  Tiedong Ma,et al.  Adaptive hybrid projective synchronization of two coupled fractional-order complex networks with different sizes , 2015, Neurocomputing.

[21]  Xing-yuan Wang,et al.  Projective synchronization of fractional order chaotic system based on linear separation , 2008 .

[22]  Y. Wang,et al.  Stability Analysis of Markovian Jumping Stochastic Cohen–Grossberg Neural Networks With Mixed Time Delays , 2008, IEEE Transactions on Neural Networks.

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

[24]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[25]  Qiankun Song,et al.  Synchronization of fractional-order memristor-based complex-valued neural networks with uncertain parameters and time delays , 2018 .

[26]  Huaguang Zhang,et al.  Global Asymptotic Stability of Recurrent Neural Networks With Multiple Time-Varying Delays , 2008, IEEE Transactions on Neural Networks.

[27]  E. Ahmed,et al.  On fractional order differential equations model for nonlocal epidemics , 2007, Physica A: Statistical Mechanics and its Applications.

[28]  Huaguang Zhang,et al.  Novel Weighting-Delay-Based Stability Criteria for Recurrent Neural Networks With Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.

[29]  Elif Demirci,et al.  A fractional order SEIR model with vertical transmission , 2011, Math. Comput. Model..

[30]  Jinde Cao,et al.  Projective synchronization of fractional-order delayed neural networks based on the comparison principle , 2018, Advances in Difference Equations.

[31]  Peifeng Niu,et al.  Global Mittag-Leffler projective synchronization for fractional-order neural networks: an LMI-based approach , 2016 .

[32]  P. Butzer,et al.  AN INTRODUCTION TO FRACTIONAL CALCULUS , 2000 .

[33]  Manfeng Hu,et al.  Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control , 2015 .

[34]  I. Podlubny Fractional differential equations , 1998 .

[35]  I. Stamova Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays , 2014, Nonlinear Dynamics.

[36]  Liping Chen,et al.  Comparison principles and stability of nonlinear fractional-order cellular neural networks with multiple time delays , 2015, Neurocomputing.