Dynamical Analysis of Competitive Neural Systems With Hybrid Time Scales and Distributed Delays

This paper studies a class of competitive neural systems with hybrid time scales and distributed delays. Without assuming the active functions to be differentiable and bounded, we prove the existence and uniqueness of the equilibrium, and derive a sufficient condition to ensure the global asymptotic stability of the neural systems. Finally, one numerical example and the computational simulations are given to illustrate the results.

[1]  Zhigang Zeng,et al.  Global asymptotic stability and global exponential stability of delayed cellular neural networks , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Liqun Qi,et al.  Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis , 2004, IEEE Trans. Neural Networks.

[3]  Jinde Cao Global stability conditions for delayed CNNs , 2001 .

[4]  Cui Bao-tong Global exponential stability of competitive neural networks with different time-scales , 2008 .

[5]  Hongtao Lu,et al.  Global exponential stability of delayed competitive neural networks with different time scales , 2005, Neural Networks.

[6]  Haijun Jiang,et al.  Global asymptotic and robust stability of inertial neural networks with proportional delays , 2018, Neurocomputing.

[7]  Zhigang Zeng,et al.  Lagrange stability of neural networks with memristive synapses and multiple delays , 2014, Inf. Sci..

[8]  Min Wu,et al.  Further results on exponential stability of neural networks with time-varying delay , 2015, Appl. Math. Comput..

[9]  Jinde Cao,et al.  Multistability of competitive neural networks with time-varying and distributed delays , 2009 .

[10]  E. Sánchez,et al.  Input-to-state stability (ISS) analysis for dynamic neural networks , 1999 .

[11]  Anke Meyer-Bäse,et al.  Singular Perturbation Analysis of Competitive Neural Networks with Different Time Scales , 1996, Neural Computation.

[12]  Jingfeng Wang,et al.  Global Lagrange stability for inertial neural networks with mixed time-varying delays , 2017, Neurocomputing.

[13]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

[14]  B. Pourciau Hadamard's theorem for locally Lipschitzian maps , 1982 .

[15]  Ruya Samli,et al.  A new delay-independent condition for global robust stability of neural networks with time delays , 2015, Neural Networks.

[16]  B. V. K. Vijaya Kumar,et al.  Emulating the dynamics for a class of laterally inhibited neural networks , 1989, Neural Networks.