Stability and bifurcation analysis for a neural network model with discrete and distributed delays

Mathematical Methods in the Applied Sciences

Volumn 36, Issue 1, 2013, Pages 49-59

  Du, Yanke ^a   Xu, Rui ^a   Liu, Qiming ^a  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

Author keywords

Hopf bifurcation; neural network; stability; time delay

Indexed keywords

BIFURCATING PERIODIC SOLUTIONS; BIFURCATION PARAMETER; CHAOTIC DYNAMICS; CHARACTERISTIC EQUATION; CHARACTERISTIC SEQUENCE; COMPLEX DYNAMICS; DISCRETE AND DISTRIBUTED DELAYS; DISCRETE TIME DELAY; LOCAL STABILITY; NEURAL NETWORK MODEL; STABILITY AND BIFURCATION ANALYSIS; TRIVIAL EQUILIBRIUM;

CONVERGENCE OF NUMERICAL METHODS; DYNAMICS; NEURAL NETWORKS; STABILITY; TIME DELAY;

HOPF BIFURCATION;

EID: 84872836818     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.2568     Document Type: Article

References (21)

1. Hopfield J,. Neurons with graded response have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Sciences of the United States of America 1984; 81: 3088-3092. (Pubitemid 14109528)
2. Huang L, Wu J,. Dynamics of inhibitory artificial neural networks with threshold nonlinearity. Fields Institute Communications 2001; 29: 235-243.
3. Huang L, Wu J,. The role of threshold in preventing delay-induced oscillations of frustrated neural networks with McCulloch-Pitts nonlinearity. International Journal of Mathematics, Game Theory and Algebra 2001; 11: 71-100.
4. Balasubramaniam P, Kalpana M, Rakkiyappan R,. Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays. Mathematical and Computer Modelling 2011; 53: 839-853.
5. Balasubramaniam P, Nagamani G, Rakkiyappan R,. Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term. Communications in Nonlinear Science and Numerical Simulation 2011; 16: 4422-4437.
6. Gopalsamy K,. Leakage delays in BAM. Journal of Mathematical Analysis and Applications 2007; 325: 1117-1132. (Pubitemid 44615832)
7. Li X, Cao J,. Delay-dependent stability of neural networks of neutral type with time delay in the leakage term. Nonlinearity 2010; 23: 1709-1726.
8. Li X, Fu X, Balasubramaniam P, et al,. Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations. Nonlinear Analysis: Real World Applications 2010; 11: 4092-4108.
9. Li X, Rakkiyappanb R, Balasubramaniam P,. Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. Journal of the Franklin Institute 2011; 348: 135-155.
10. Peng S,. Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Nonlinear Analysis: Real World Applications 2010; 11: 2141-2151.
11. Gopalsamy K,. Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic Publishers: Dordrecht, 1992.
12. Fan D, Wei J,. Hopf bifurcation analysis in a tri-neuron network with time delay. Nonlinear Analysis: Real World Applications 2008; 9: 9-25. (Pubitemid 47562883)
13. Yan X,. Bifurcation analysis in a simplified tri-neuron BAM network model with multiple delays. Nonlinear Analysis: Real World Applications 2008; 9: 963-976. (Pubitemid 351221407)
14. Yuan S, Li X,. Stability and bifurcation analysis of an annular delayed neural network with self-connection. Neurocomputing 2010; 73: 2905-2912.
15. Zhao H, Wang L, Ma C,. Hopf bifurcation and stability analysis on discrete-time Hopfield neural network with delay. Nonlinear Analysis: Real World Applications 2008; 9: 103-113. (Pubitemid 47562889)
16. Hsua C, Yang S, Yang T,. Stability and bifurcation of a two-neuron network with distributed time delays. Nonlinear Analysis: Real World Applications 2010; 11: 1472-1490.
17. Wang B, Jian J,. Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with distributed delays. Communications in Nonlinear Science and Numerical Simulation 2010 15: 189-204.
18. Zhao H, Wang L,. Hopf bifurcation in Cohen-Grossberg neural network with distributed delays. Nonlinear Analysis: Real World Applications 2007; 8: 73-89. (Pubitemid 44584785)
19. Zhou X, Wu Y, Li Y, et al,. Stability and Hopf bifurcation analysis on a two-neuron network with discrete and distributed delays. Chaos, Solitons and Fractals 2009; 40: 1493-1505.
20. Zhu H, Huang L,. Stability and bifurcation in a tri-neuron network model with discrete and distributed delays. Applied Mathematics and Computation 2007; 188: 1742-1756. (Pubitemid 46710064)
21. Hassard B, Kazarinoff N, Wan Y,. Theory and Applications of Hopf Bifurcation. Cambridge University Press: Cambridge, 1981.