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.