New stability criteria and bifurcation analysis for nonlinear discrete-time coupled loops with multiple delays.
A detailed analysis of zero distributions in a special polynomial of the form lambda(tau)(lambda-a(1))(lambda-a(2))...(lambda-a(n))-(c+id) is proposed, where all a(i)(i=1,2,...,) have the same sign. As its applications, new criteria for asymptotic behavior of nonlinear delayed coupled systems with different topological structures are established. All possible bifurcations, including codimension-two bifurcations with 1:4/1:3 strong resonance in such a delayed difference system, are discussed. Numerical simulation gives a solid verification of the theoretical analysis.
Peng
Mingshu
M
Department of Mathematics, Beijing Jiao Tong University, Beijing 100044, People's Republic of China. mshpeng@bjtu.edu.cn
Yang
Xiaozhong
X
D000465:Algorithms; D001703:Biophysics / Q000379:methods; D008959:Models, Neurological; D015233:Models, Statistical; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology; D010825:Physics / Q000379:methods*; D013997:Time Factors