Department of Mathematics, Beijing Jiao Tong University, Beijing 100044, People's Republic of China.
Chaos. 2010 Mar;20(1):013125. doi: 10.1063/1.3339857.
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.
提出了一种特殊形式的多项式 lambda(tau)(lambda-a(1))(lambda-a(2))...(lambda-a(n))-(c+id) 中零点分布的详细分析，其中所有 a(i)(i=1,2,...,) 具有相同的符号。作为其应用，建立了具有不同拓扑结构的非线性时滞耦合系统渐近行为的新判据。讨论了这种时滞差分系统中可能发生的所有分岔，包括二维分岔和 1:4/1:3 强共振。数值模拟为理论分析提供了有力的验证。
