Backward Euler-Maruyama method for a class of stochastic Markovian jump neural networks

Stability analysis of various neural networks have been successfully applied in many fields such as parallel computing and pattern recognition. This paper is concerned with a class of stochastic Markovian jump neural networks. The general mean-square stability of Backward Euler-Maruyama method for stochastic Markovian jump neural networks is discussed. The sufficient conditions to guarantee the general mean-square stability of Backward Euler-Maruyama method are given.

[1]  Xiaodi Li,et al.  Existence and global exponential stability of periodic solution for delayed neural networks with impulsive and stochastic effects , 2010, Neurocomputing.

[2]  Chengming Huang,et al.  Exponential mean square stability of the theta approximations for neutral stochastic differential delay equations , 2015, J. Comput. Appl. Math..

[3]  Ronghua Li,et al.  Exponential stability of numerical solutions to stochastic delay Hopfield neural networks , 2010, Neurocomputing.

[4]  Junfeng Chen,et al.  Stability analysis of stochastic Markovian switching static neural networks with asynchronous mode-dependent delays , 2015, Neurocomputing.

[5]  Peng Hu,et al.  Stability of stochastic θ-methods for stochastic delay integro-differential equations , 2011, Int. J. Comput. Math..

[6]  Baocang Ding,et al.  Mean-square dissipativity of numerical methods for a class of stochastic neural networks with fractional Brownian motion and jumps , 2015, Neurocomputing.

[7]  P. Balasubramaniam,et al.  Exponential stability of stochastic reaction-diffusion uncertain fuzzy neural networks with mixed delays and Markovian jumping parameters , 2012, Expert Syst. Appl..

[8]  Yi Shen,et al.  Stability in the numerical simulation of stochastic delayed Hopfield neural networks , 2012, Neural Computing and Applications.

[9]  Yi Shen,et al.  Stability of the split-step backward Euler scheme for stochastic delay integro-differential equations with Markovian switching , 2011 .

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

[11]  Paul C. Bressloff,et al.  Metastability in a Stochastic Neural Network Modeled as a Velocity Jump Markov Process , 2013, SIAM J. Appl. Dyn. Syst..

[12]  Andrew M. Stuart,et al.  Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations , 2002, SIAM J. Numer. Anal..

[13]  X. Lou,et al.  Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters , 2009 .

[14]  Song Zhu,et al.  Non-fragile observer-based H∞ control for neutral stochastic hybrid systems with time-varying delay , 2011, Neural Computing and Applications.

[15]  John J. Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities , 1999 .

[16]  T. A. Averina,et al.  Numerical solution of stochastic differential equations in the sense of Stratonovich in an amorphization crystal lattice model , 2015 .

[17]  Stefano Panzieri,et al.  Urban traffic flow forecasting through statistical and neural network bagging ensemble hybrid modeling , 2015, Neurocomputing.

[18]  Jinde Cao,et al.  Stability of bidirectional associative memory neural networks with Markov switching via ergodic method and the law of large numbers , 2015, Neurocomputing.

[19]  Quanxin Zhu,et al.  Almost sure exponential stability of numerical solutions to stochastic delay Hopfield neural networks , 2015, Appl. Math. Comput..

[20]  Zhigang Zeng,et al.  Dynamics Analysis of a Class of Memristor-Based Recurrent Networks with Time-Varying Delays in the Presence of Strong External Stimuli , 2011, Neural Processing Letters.

[21]  Lei Liu,et al.  Exponential Stability of Uncertain Stochastic Neural Networks with Markovian Switching , 2010, Neural Processing Letters.

[22]  Yi Shen,et al.  Stability of Stochastic $$\theta $$-Methods for Stochastic Delay Hopfield Neural Networks Under Regime Switching , 2013, Neural Processing Letters.

[23]  Raman Manivannan,et al.  Robust passivity analysis for stochastic impulsive neural networks with leakage and additive time-varying delay components , 2015, Appl. Math. Comput..

[24]  Xin-She Yang,et al.  Computational Intelligence and Metaheuristic Algorithms with Applications , 2014, TheScientificWorldJournal.

[25]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[26]  Dongsheng Guo,et al.  Common nature of learning between BP-type and Hopfield-type neural networks , 2015, Neurocomputing.

[27]  Feng Jiang,et al.  Stochastic θ-Methods for a Class of Jump-Diffusion Stochastic Pantograph Equations with Random Magnitude , 2014, TheScientificWorldJournal.