Global attractivity of memristor-based fractional-order neural networks

Abstract Some dynamical properties, especially the global attractivity, of memristor-based fractional-order neural networks (FNN) are discussed. By using Filippov solutions, the existence of memristor-based FNN's solutions is firstly guaranteed under a growth condition. With non-Lipschitz neuron activations, different dynamics of memristor-based FNN are analyzed by employing the Lyapunov functionals. Then, a local Mittag-Leffler stability condition is presented for memristor-based FNN. To obtain the global dynamical properties, the global boundedness of memristor-based FNN is discussed. Further, with proposing additional conditions, the global attractivity of memristor-based FNN is realized. To verify the effectiveness of the obtained results, three numerical examples are given in the end.

[1]  Xibing Kang,et al.  Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays. , 2013, ISA transactions.

[2]  Eva Kaslik,et al.  Nonlinear dynamics and chaos in fractional-order neural networks , 2012, Neural Networks.

[3]  Jinde Cao,et al.  Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays , 2014, Cognitive Neurodynamics.

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

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

[6]  Zhixia Ding,et al.  Global dissipativity of fractional-order neural networks with time delays and discontinuous activations , 2016, Neurocomputing.

[7]  Yong-sheng Ding,et al.  A generalized Gronwall inequality and its application to a fractional differential equation , 2007 .

[8]  Junzhi Yu,et al.  Global stability analysis of fractional-order Hopfield neural networks with time delay , 2015, Neurocomputing.

[9]  Hao Yan,et al.  Programmable nanowire circuits for nanoprocessors , 2011, Nature.

[10]  Yuriy V. Pershin,et al.  Memory effects in complex materials and nanoscale systems , 2010, 1011.3053.

[11]  Zhigang Zeng,et al.  Exponential synchronization of memristor-based recurrent neural networks with time delays , 2011, Neurocomputing.

[12]  Wei Zhang,et al.  Stability and synchronization of memristor-based coupling neural networks with time-varying delays via intermittent control , 2016, Neurocomputing.

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

[14]  Alain Oustaloup,et al.  Fractional system identification for lead acid battery state of charge estimation , 2006, Signal Process..

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

[16]  Richard L. Magin,et al.  Fractional calculus models of complex dynamics in biological tissues , 2010, Comput. Math. Appl..

[17]  Zhigang Zeng,et al.  Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays , 2012, Neural Networks.

[18]  Zhigang Zeng,et al.  Global Mittag-Leffler stabilization of fractional-order bidirectional associative memory neural networks , 2016, Neurocomputing.

[19]  Jinde Cao,et al.  A feedback neural network for solving convex constraint optimization problems , 2008, Appl. Math. Comput..

[20]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[21]  Thierry Poinot,et al.  Fractional modelling and identification of thermal systems , 2011, Signal Process..

[22]  Chuandong Li,et al.  A Recurrent Neural Network for Solving Bilevel Linear Programming Problem , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[23]  Zhigang Zeng,et al.  Synchronization control of a class of memristor-based recurrent neural networks , 2012, Inf. Sci..

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

[25]  Eva Kaslik,et al.  Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis , 2011, Neural Networks.

[26]  S. Das,et al.  Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel , 2010, Appl. Math. Comput..

[27]  J. Cortés.  Discontinuous dynamical systems , 2008, IEEE Control Systems.

[28]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[29]  Johnny Henderson,et al.  Fractional functional differential inclusions with finite delay , 2009 .

[30]  Farnood Merrikh-Bayat,et al.  Programming of memristor crossbars by using genetic algorithm , 2011, WCIT.

[31]  Morteza Dardel,et al.  Vibration control of a nonlinear beam with a nonlinear energy sink , 2016 .

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

[33]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[34]  Xinghuo Yu,et al.  A Generalized Hopfield Network for Nonsmooth Constrained Convex Optimization: Lie Derivative Approach , 2016, IEEE Transactions on Neural Networks and Learning Systems.

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

[36]  Qing Wang,et al.  Stability analysis of fractional-order Hopfield neural networks with discontinuous activation functions , 2016, Neurocomputing.

[37]  Yongguang Yu,et al.  Mittag-Leffler stability of fractional-order Hopfield neural networks , 2015 .

[38]  Bruce J. West,et al.  Fractional Langevin model of memory in financial markets. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[40]  Sohrab Effati,et al.  Existence and stability analysis of bifurcating periodic solutions in a delayed five-neuron BAM neural network model , 2013 .

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

[42]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

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

[44]  Tiedong Ma,et al.  Dynamic analysis of a class of fractional-order neural networks with delay , 2013, Neurocomputing.

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