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

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 furt...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2019-01, Vol.2019 (2019), p.1-14
Main Authors: Chen, Cun, Ren, Jingli, Li, Xueping
Format: Article
Language:English
Subjects:
Analysis
Deformation
Dynamics
Earthquakes
Engineering
Fault lines
Geological faults
Hopf bifurcation
Knopoff, Leon
Mathematical models
Mechanics
Periodic variations
Perturbation methods
Stiffness
Toruses
Transform faults
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Summary: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.
ISSN:1076-2787
1099-0526
DOI:10.1155/2019/5253496