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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Main Authors: Cun Chen, Xueping Li, Jingli Ren
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2019/5253496
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author Cun Chen
Xueping Li
Jingli Ren
author_facet Cun Chen
Xueping Li
Jingli Ren
author_sort Cun Chen
collection DOAJ
description 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.
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spelling doaj-art-a7e790ca156d402fbc70d79d83aaea012025-08-20T02:20:56ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/52534965253496Complex Dynamical Behaviors in a Spring-Block Model with Periodic PerturbationCun Chen0Xueping Li1Jingli Ren2School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, ChinaSchool of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, ChinaSchool of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, ChinaA 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.http://dx.doi.org/10.1155/2019/5253496
spellingShingle Cun Chen
Xueping Li
Jingli Ren
Complex Dynamical Behaviors in a Spring-Block Model with Periodic Perturbation
Complexity
title Complex Dynamical Behaviors in a Spring-Block Model with Periodic Perturbation
title_full Complex Dynamical Behaviors in a Spring-Block Model with Periodic Perturbation
title_fullStr Complex Dynamical Behaviors in a Spring-Block Model with Periodic Perturbation
title_full_unstemmed Complex Dynamical Behaviors in a Spring-Block Model with Periodic Perturbation
title_short Complex Dynamical Behaviors in a Spring-Block Model with Periodic Perturbation
title_sort complex dynamical behaviors in a spring block model with periodic perturbation
url http://dx.doi.org/10.1155/2019/5253496
work_keys_str_mv AT cunchen complexdynamicalbehaviorsinaspringblockmodelwithperiodicperturbation
AT xuepingli complexdynamicalbehaviorsinaspringblockmodelwithperiodicperturbation
AT jingliren complexdynamicalbehaviorsinaspringblockmodelwithperiodicperturbation