Stability analysis of two-dimensional neutral-type Cohen–Grossberg BAM neural networks

Two-dimensional system model represents a wide range of practical systems, such as image data processing and transmission, thermal processes, gas absorption and water stream heating. Moreover, there are few dynamical discussions for the two-dimensional neutral-type Cohen–Grossberg BAM neural networks. Hence, in this paper, our purpose is to investigate the stability of two-dimensional neutral-type Cohen–Grossberg BAM neural networks. The first objective is to construct mathematical models to illustrate the two-dimensional structure and the neutral-type delays in Cohen–Grossberg BAM neural networks. Then, a sufficient condition is given to achieve the stability of two-dimensional neutral-type continuous Cohen–Grossberg BAM neural networks. Finally, simulation results are given to illustrate the usefulness of the developed criteria.

[1]  Jinde Cao,et al.  A New Framework for Analysis on Stability and Bifurcation in a Class of Neural Networks With Discrete and Distributed Delays , 2015, IEEE Transactions on Cybernetics.

[2]  Zhigang Zeng,et al.  Robust stability analysis of interval fuzzy Cohen-Grossberg neural networks with piecewise constant argument of generalized type , 2012, Neural Networks.

[3]  Zhigang Zeng,et al.  Exponential Stabilization of Memristive Neural Networks With Time Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[4]  Zidong Wang,et al.  State estimation for two‐dimensional complex networks with randomly occurring nonlinearities and randomly varying sensor delays , 2014 .

[5]  Tingwen Huang,et al.  Event-Triggering Sampling Based Leader-Following Consensus in Second-Order Multi-Agent Systems , 2015, IEEE Transactions on Automatic Control.

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

[7]  Wan-Tong Li,et al.  Stability and uniqueness of traveling wavefronts in a two-dimensional lattice differential equation with delay , 2009, Appl. Math. Comput..

[8]  Jinde Cao,et al.  Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[9]  Junzhi Yu,et al.  Bifurcation analysis of a two-dimensional simplified Hodgkin–Huxley model exposed to external electric fields , 2012, Neural Computing and Applications.

[10]  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.

[11]  Yun Zou,et al.  Decentralized H-infinity state feedback control for discrete-time singular large-scale systems , 2010 .

[13]  Nasser Mikaeilvand,et al.  Solving fuzzy partial differential equations by fuzzy two-dimensional differential transform method , 2012, Neural Computing and Applications.

[14]  Haijun Jiang,et al.  Finite-time synchronization of delayed neural networks with Cohen-Grossberg type based on delayed feedback control , 2014, Neurocomputing.

[15]  Zhigang Zeng,et al.  Improved conditions for global exponential stability of recurrent neural networks with time-varying delays , 2006, IEEE Transactions on Neural Networks.

[16]  David J. Hill,et al.  Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks , 2015, Neural Networks.

[17]  Shengyuan Xu,et al.  Positive real control for 2-D discrete delayed systems via output feedback controllers , 2008 .

[18]  Kamal Jamshidi,et al.  Traffic signal timing using two-dimensional correlation, neuro-fuzzy and queuing based neural networks , 2007, Neural Computing and Applications.

[19]  Panos Louvieris,et al.  Robust Synchronization for 2-D Discrete-Time Coupled Dynamical Networks , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Y Shapira,et al.  Observations and modeling of synchronized bursting in two-dimensional neural networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Cishen Zhang,et al.  Hinfinity control and robust stabilization of two-dimensional systems in Roesser models , 2001, Autom..

[22]  Wei Xing Zheng,et al.  Generalized H2 fault detection for two-dimensional Markovian jump systems , 2012, Autom..

[23]  Jinde Cao,et al.  Robust Stability of Switched Cohen–Grossberg Neural Networks With Mixed Time-Varying Delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[24]  Rong Zhu,et al.  A Two-Dimensional Flow Sensor with Integrated Micro Thermal Sensing Elements and a Back Propagation Neural Network , 2013, Sensors.

[25]  Ligang Wu,et al.  Sliding mode control of two-dimensional systems in Roesser model , 2008 .

[26]  Abdellah Benzaouia,et al.  Stabilization of 2D saturated systems by state feedback control , 2010, Multidimens. Syst. Signal Process..

[27]  Shengyuan Xu,et al.  Delay-dependent stability of neutral type neural networks with distributed delays , 2009, Neurocomputing.

[28]  Yurong Liu,et al.  State estimation for jumping recurrent neural networks with discrete and distributed delays , 2009, Neural Networks.

[29]  W. H. Young.  On Classes of Summable Functions and their Fourier Series , 1912 .