Mutual synchronization is a ubiquitous phenomenon that exists in various natural systems. The individual participants in this process can be modeled as oscillators, which interact by discrete pulses. In this paper, we...Mutual synchronization is a ubiquitous phenomenon that exists in various natural systems. The individual participants in this process can be modeled as oscillators, which interact by discrete pulses. In this paper, we analyze the synchronization condition of two- and multi-oscillators system, and propose a linear pulse-coupled oscillators model. We prove that the proposed model can achieve synchronization for almost all conditions. Numerical simulations are also included to investigate how different model parameters affect the synchronization. We also discuss the implementation of the model as a new approach for time synchronization in wireless sensor networks.展开更多
Unstable attractors are a novel type of attractor with local unstable dynamics, but with positive measures of basins.Here, we introduce local contracting dynamics by slightly modifying the function which mediates the ...Unstable attractors are a novel type of attractor with local unstable dynamics, but with positive measures of basins.Here, we introduce local contracting dynamics by slightly modifying the function which mediates the interactions among the oscillators. Thus, the property of unstable attractors can be controlled through the cooperation of expanding and contracting dynamics. We demonstrate that one certain type of unstable attractor is successfully controlled through this simple modification. Specifically, the staying time for unstable attractors can be prolonged, and we can even turn the unstable attractors into stable attractors with predictable basin sizes. As an application, we demonstrate how to realize the switching dynamics that is only sensitive to the finite size perturbations.展开更多
文摘Mutual synchronization is a ubiquitous phenomenon that exists in various natural systems. The individual participants in this process can be modeled as oscillators, which interact by discrete pulses. In this paper, we analyze the synchronization condition of two- and multi-oscillators system, and propose a linear pulse-coupled oscillators model. We prove that the proposed model can achieve synchronization for almost all conditions. Numerical simulations are also included to investigate how different model parameters affect the synchronization. We also discuss the implementation of the model as a new approach for time synchronization in wireless sensor networks.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11502200 and 91648101)the Fundamental Research Funds for the Central Universities,China(Grant No.3102018zy012)
文摘Unstable attractors are a novel type of attractor with local unstable dynamics, but with positive measures of basins.Here, we introduce local contracting dynamics by slightly modifying the function which mediates the interactions among the oscillators. Thus, the property of unstable attractors can be controlled through the cooperation of expanding and contracting dynamics. We demonstrate that one certain type of unstable attractor is successfully controlled through this simple modification. Specifically, the staying time for unstable attractors can be prolonged, and we can even turn the unstable attractors into stable attractors with predictable basin sizes. As an application, we demonstrate how to realize the switching dynamics that is only sensitive to the finite size perturbations.
