Nonlinear Dynamics

, Volume 56, Issue 1–2, pp 127–144 | Cite as

Effects of small world connection on the dynamics of a delayed ring network

Original Paper


This paper presents a detailed analysis on the dynamics of a ring network with small world connection. On the basis of Lyapunov stability approach, the asymptotic stability of the trivial equilibrium is first investigated and the delay-dependent criteria ensuring global stability are obtained. The existence of Hopf bifurcation and the stability of periodic solutions bifurcating from the trivial equilibrium are then analyzed. Further studies are paid to the effects of small world connection on the stability interval and the stability of periodic solution. In particular, some complex dynamical phenomena due to short-cut strength are observed numerically, such as: period-doubling bifurcation and torus breaking to chaos, the coexistence of multiple periodic solutions, multiple quasi-periodic solutions, and multiple chaotic attractors. The studies show that small world connection may be used as a simple but efficient “switch” to control the dynamics of a system.


Ring network Small world Global stability Bifurcation Chaos 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.College of MathematicsJilin UniversityChangchunChina
  2. 2.Department of Mechanics at School of ScienceBeijing Institute of TechnologyBeijingChina
  3. 3.The Singapore-MIT Alliance (SMA)SingaporeSingapore
  4. 4.Institute of Vibration Engineering ResearchNanjing University of Aeronautics and AstronauticsNanjingChina

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