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Complex Dynamical Behaviors in a Spring-Block Model with Periodic Perturbation

Author

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  • Cun Chen
  • Xueping Li
  • Jingli Ren

Abstract

A generalization of a Burridge-Knopoff spring-block model is investigated to illustrate the dynamics of transform faults. The model can undergo Hopf bifurcation and fold bifurcation of limit cycles. Considering the cyclical nature of the spring stiffness, the model with periodic perturbation is further explored via a continuation technique and numerical bifurcation analysis. It is shown that the periodic perturbation induces abundant dynamics, the existence, the switch, and the coexistence of multiple attractors including periodic solutions with various periods, quasiperiodic solutions, chaotic solutions through torus destruction, or cascade of period doublings. Throughout the results obtained, one can see that the system manifests complex dynamical behaviors such as chaos, self-organized criticality, and the transition of dynamical behaviors when it comes to periodic perturbations. Even very small variation of a parameter can result in radical changes of the dynamics, which provides a new insight into the fault dynamics.

Suggested Citation

  • Cun Chen & Xueping Li & Jingli Ren, 2019. "Complex Dynamical Behaviors in a Spring-Block Model with Periodic Perturbation," Complexity, Hindawi, vol. 2019, pages 1-14, March.
  • Handle: RePEc:hin:complx:5253496
    DOI: 10.1155/2019/5253496
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    References listed on IDEAS

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    1. Peter B. Kelemen & Greg Hirth, 2007. "A periodic shear-heating mechanism for intermediate-depth earthquakes in the mantle," Nature, Nature, vol. 446(7137), pages 787-790, April.
    2. Cun Chen & Shaokang Guan & Liying Zhang, 2018. "Complex Dynamical Behavior in the Shear-Displacement Model for Bulk Metallic Glasses during Plastic Deformation," Complexity, Hindawi, vol. 2018, pages 1-13, December.
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    Cited by:

    1. Shaowen Yao & Zhibo Cheng, 2019. "Plastic Dynamical Model for Bulk Metallic Glasses," Complexity, Hindawi, vol. 2019, pages 1-7, December.

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