Finite-Time Stability of Fractional-Order Neural Networks with Delay

Finite-time stability of a class of fractional-order neural networks is investigated in this paper. By Laplace transform, the generalized Gronwall inequality and estimates of Mittag-Leffler functions, sufficient conditions are pre - sented to ensure the finite-time stability of such neural models with the Caputo fractional derivatives. Furthermore, results about asymptotical stability of fractional-order neural models are also obtained.

[1]  Zhen Wang,et al.  Chaos and hyperchaos in fractional-order cellular neural networks , 2012, Neurocomputing.

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

[3]  Hongyong Zhao,et al.  Dynamics of Cohen–Grossberg neural networks with variable and distributed delays , 2007 .

[4]  R. Wu Exponential convergence of BAM neural networks with time-varying coefficients and distributed delays , 2010 .

[5]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

[6]  Huijun Gao,et al.  A Constrained Evolutionary Computation Method for Detecting Controlling Regions of Cortical Networks , 2012, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[7]  Mohammad Bagher Menhaj,et al.  Fractional-Order Hopfield Neural Networks , 2008, ICONIP.

[8]  Zidong Wang,et al.  Pinning control of fractional-order weighted complex networks. , 2009, Chaos.

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

[10]  P. Arena,et al.  Chaotic behavior in noninteger-order cellular neural networks , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[12]  Jiang Wei,et al.  Some results of the degenerate fractional differential system with delay , 2011, Comput. Math. Appl..

[13]  Thomas J. Anastasio,et al.  The fractional-order dynamics of brainstem vestibulo-oculomotor neurons , 1994, Biological Cybernetics.

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

[15]  Huijun Gao,et al.  Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings , 2013, IEEE Transactions on Cybernetics.

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

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

[18]  Jinde Cao,et al.  Global exponential stability of discrete-time recurrent neural network for solving quadratic programming problems subject to linear constraints , 2011, Neurocomputing.

[19]  Jinde Cao,et al.  A Novel Recurrent Neural Network with Finite-Time Convergence for Linear Programming , 2010, Neural Computation.

[20]  George A. Anastassiou,et al.  Fractional neural network approximation , 2012, Comput. Math. Appl..

[21]  A. Fairhall,et al.  Fractional differentiation by neocortical pyramidal neurons , 2008, Nature Neuroscience.

[22]  M. De la Sen,et al.  About Robust Stability of Caputo Linear Fractional Dynamic Systems with Time Delays through Fixed Point Theory , 2011 .

[23]  Aleksandar M. Spasic,et al.  Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach , 2009, Math. Comput. Model..