Stability Analysis of a Class of Fractional-order Neural Networks

In this paper, the problems of the existence and uniqueness of solutions and stability for a class of fractional-order neural networks are studied by using Banach fixed point principle and analysis technique, respectively. A sufficient condition is given to ensure the existence and uniqueness of solutions and uniform stability of solutions for fractional-order neural networks with variable coefficients and multiple time delays. The obtained results improve and extend some previous works to some extent, and they are easy to check in practice. An illustrative example is presented to show the validity and application of the proposed results. DOI : http://dx.doi.org/10.11591/telkomnika.v12i2.4409

[1]  D Harikrishna,et al.  Dynamic Stability Enhancement of Power Systems Using Neural-Network Controlled Static-Compensator , 2012 .

[2]  Yuehua Yu,et al.  New convergence behavior of high-order hopfield neural networks with time-varying coefficients , 2008 .

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

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

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

[6]  M. Tan,et al.  Global exponential stability of periodic solution of neural network with variable coefficients and time-varying delays , 2009 .

[7]  Hu Sheng,et al.  Fractional-order variational optical flow model for motion estimation , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[9]  P. Miškinis.  Modelling linear reactions in inhomogeneous catalytic systems , 2013, Journal of Mathematical Chemistry.

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

[11]  Francesco Pappalardo,et al.  Fractional-order simulation tool for the brainstem vestibulo-ocular reflex (VOR) , 2012, Signal Image Video Process..

[12]  Miguel A. García-González,et al.  An application of fractional differintegration to heart rate variability time series , 2013, Comput. Methods Programs Biomed..

[13]  Zhidong Teng,et al.  Existence and global exponential stability of almost periodic solution for cellular neural networks with variable coefficients and time-varying delays , 2005, IEEE Transactions on Neural Networks.

[14]  Lin Niu,et al.  Adaptive Neural Network Generalized Predictive Control for Unknown Nonlinear System , 2013 .

[15]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[16]  Jin-Rong Liang,et al.  Time-changed geometric fractional Brownian motion and option pricing with transaction costs , 2012 .

[17]  Zhidong Teng,et al.  Global eponential stability of cellular neural networks with time-varying coefficients and delays , 2004, Neural Networks.

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

[19]  Bingwen Liu,et al.  Exponential convergence for a class of delayed cellular neural networks with time-varying coefficients , 2008 .

[20]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[21]  Zhu Ling,et al.  Adaptive RBFNN Formation Control of Multi-mobile Robots with Actuator Dynamics , 2013 .

[22]  Wen Chen,et al.  A fractional-order model on new experiments of linear viscoelastic creep of Hami Melon , 2013, Comput. Math. Appl..

[23]  Rainer Schöbel,et al.  A note on the use of fractional Brownian motion for financial modeling , 2013 .

[24]  Ma Xi-Kui,et al.  Transfer function modeling and analysis of the open-loop Buck converter using the fractional calculus , 2013 .

[25]  Jinde Cao,et al.  Boundedness and stability for recurrent neural networks with variable coefficients and time-varying delays , 2003 .