Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays

Proportional delay is a kind of unbounded time-varying delay, which is different from unbounded distributed delays. A class of hybrid BAM neural networks with proportional delays is concerned in this paper. First, by choosing suitable nonlinear variable transformations, the hybrid BAM neural networks with proportional delays can be equivalently transformed into the hybrid BAM neural networks with constant delays and variable coefficients. Then, in virtue of Brouwer?s fixed point theorem, the existence and uniqueness of equilibrium point of the system are proved. Furthermore, by constructing appropriate delay differential inequalities, several new delay-independent and delay-dependent global exponential stability sufficient conditions of equilibrium point of the system are obtained, and can be easily checked by simple algebraic calculation. Finally, several numerical examples are given to illustrate the effectiveness the obtained results and less conservative than some existing results.

[1]  Yunkang Liu,et al.  Asymptotic behaviour of functional-differential equations with proportional time delays , 1996, European Journal of Applied Mathematics.

[2]  Zhengqiu Zhang,et al.  Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays , 2012, Neural Networks.

[3]  Liqun Zhou,et al.  Delay-Dependent Exponential Stability of Cellular Neural Networks with Multi-Proportional Delays , 2012, Neural Processing Letters.

[4]  B Kosko,et al.  Adaptive bidirectional associative memories. , 1987, Applied optics.

[5]  Liqun Zhou.  Dissipativity of a class of cellular neural networks with proportional delays , 2013 .

[6]  Jinde Cao,et al.  Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays , 2014, Neural Networks.

[7]  Shan Gao,et al.  Global Exponential Stability for Impulsive BAM Neural Networks with Distributed Delays on Time Scales , 2010, Neural Processing Letters.

[8]  Yonggui Kao,et al.  Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction-Diffusion Cohen-Grossberg Neural Networks , 2012, Neural Processing Letters.

[9]  X. Liao,et al.  Convergence dynamics of hybrid bidirectional associative memory neural networks with distributed delays , 2003 .

[10]  Cheng-Zhong Xu,et al.  A robust packet scheduling algorithm for proportional delay differentiation services , 2004, IEEE Global Telecommunications Conference, 2004. GLOBECOM '04..

[11]  Arieh Iserles,et al.  The asymptotic behaviour of certain difference equations with proportional delays , 1994 .

[12]  Zhengqiu Zhang,et al.  Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays , 2011, Neural Networks.

[13]  G. Derfel,et al.  Kato Problem for Functional-Differential Equations and Difference Schrödinger Operators , 1990 .

[14]  Chuandong Li,et al.  Delay-dependent exponential stability analysis of bi-directional associative memory neural networks with time delay: an LMI approach , 2005 .

[15]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[16]  Zhengqiu Zhang,et al.  New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type , 2012, Neurocomputing.

[17]  Chuandong Li,et al.  Impulsive effects on stability of high-order BAM neural networks with time delays , 2011, Neurocomputing.

[18]  L. Fox,et al.  On a Functional Differential Equation , 1971 .

[19]  Jinde Cao,et al.  Matrix measure based stability criteria for high-order neural networks with proportional delay , 2015, Neurocomputing.

[20]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Ewing L. Lusk,et al.  Experiments with resolution-based theorem-proving algorithms , 1982 .

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

[23]  Liqun Zhou.  Global asymptotic stability of cellular neural networks with proportional delays , 2014 .

[24]  Yixian Yang,et al.  Asymptotic stability of cellular neural networks with multiple proportional delays , 2014, Appl. Math. Comput..

[25]  Sabri Arik,et al.  An improved robust stability result for uncertain neural networks with multiple time delays , 2014, Neural Networks.

[26]  Chaojie Li,et al.  Exponential stability of stochastic high-order BAM neural networks with time delays and impulsive effects , 2013, Neural Computing and Applications.

[27]  Hao Liu,et al.  New stability criteria for BAM neural networks with time-varying delays , 2009, Neurocomputing.

[28]  Rajendran Samidurai,et al.  Global asymptotic stability of BAM neural networks with mixed delays and impulses , 2009, Appl. Math. Comput..

[29]  D. Gale.  The Game of Hex and the Brouwer Fixed-Point Theorem , 1979 .

[30]  Kwok-Wo Wong,et al.  Robust stability of interval bidirectional associative memory neural network with time delays , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[31]  Bao Shi,et al.  Exponential stability of BAM neural networks with time-varying delays , 2008 .

[32]  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.

[33]  Jinde Cao,et al.  Novel LMI-Based Condition on Global Asymptotic Stability for a Class of Cohen–Grossberg BAM Networks With Extended Activation Functions , 2014, IEEE Transactions on Neural Networks and Learning Systems.