Birhythmic 振子个体及群体行为的动力学研究

Birhythmic振子动力学的研究是国际上最活跃的科学前沿之一。迄今为止，绝大部分的成果都是从统计角度来研究系统响应。虽然响应均值，方差等确定性指标可以直观地展现系统响应的性质，但是这些指标有时很难反映出噪声对于多稳态系统的本质影响。基于此，本项目拟通过最大化系统概率密度函数得出其对应的最可能轨迹作为随机birhythmic系统的确定性指标，来研究系统的响应、分岔和首次穿越时间问题。同时，探究耦合birhythmic振子网络的爆炸性行为及奇异态的产生机制，尝试发展用于判定耦合birhythmic振子网络上爆炸性行为发生的临界条件，奇异态是否存在的分析方法。目标是初步建立birhythmic系统动力学的理论分析和数值方法，推动随机动力学和网络动力学的发展，为生物、工程等领域提供重要的理论基础和分析方法。

The study of birhythmic dynamics is currently one of the most active scientific frontiers in the world. Till now, most of the achievements have been made from a statistical perspective to study the response of systems. Although the deterministic indexes including the mean value and variance of the response can visually display the characteristic of the system response, these indexes can hardly reflect the influence of noise on the system under stochastic disturbance. Based on this, the project intends to investigate different types of system responses by using the most probable trajectories corresponding to the maximum of the probability density function of the system as the deterministic index of the stochastic birhythmic system. Furthermore, we would like to explore the mechanisms in the network of coupled birhythmic oscillators through which the explosive phenomena and chimera state occur, and develop the analytical method to determine the critical conditions for the occurrence of explosive behaviors and the existence of chimera state. The objective of this project is to establish the theoretical and numerical methods for the birhythmic system, to probe a pragmatic research approach for stochastic dynamics and network dynamics, and to provide important theoretical and practical significance for real fields such as biology and engineering.