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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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| 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. |
| format | Article |
| id | doaj-art-a7e790ca156d402fbc70d79d83aaea01 |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| 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 |
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