Thakur Bhumika, Sharma Devendra, Sen Abhijit
Institute for Plasma Research, Bhat, Gandhinagar 382428, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):042904. doi: 10.1103/PhysRevE.90.042904. Epub 2014 Oct 6.
We investigate the influence of time-delayed coupling on the nature of the aging transition in a system of coupled oscillators that have a mix of active and inactive oscillators, where the aging transition is defined as the gradual loss of collective synchrony as the proportion of inactive oscillators is increased. We start from a simple model of two time-delay coupled Stuart-Landau oscillators that have identical frequencies but are located at different distances from the Hopf bifurcation point. A systematic numerical and analytic study delineates the dependence of the critical coupling strength (at which the system experiences total loss of synchrony) on time delay and the average distance of the system from the Hopf bifurcation point. We find that time delay can act to facilitate the aging transition by lowering the threshold coupling strength for amplitude death in the system. We then extend our study to larger systems of globally coupled active and inactive oscillators including an infinite system in the thermodynamic limit. Our model system and results can provide a useful paradigm for understanding the functional robustness of diverse physical and biological systems that are prone to aging transitions.
我们研究了时间延迟耦合对具有活跃和非活跃振荡器混合的耦合振荡器系统中老化转变性质的影响，其中老化转变被定义为随着非活跃振荡器比例的增加，集体同步性逐渐丧失。我们从一个简单的两个时间延迟耦合的斯图尔特 - 兰道振荡器模型开始，它们具有相同的频率，但与霍普夫分岔点的距离不同。一项系统的数值和分析研究描绘了临界耦合强度（系统经历完全同步丧失时的耦合强度）对时间延迟以及系统与霍普夫分岔点平均距离的依赖性。我们发现时间延迟可以通过降低系统中振幅死亡的阈值耦合强度来促进老化转变。然后我们将研究扩展到更大的全局耦合活跃和非活跃振荡器系统，包括热力学极限下的无限系统。我们的模型系统和结果可以为理解容易发生老化转变的各种物理和生物系统的功能稳健性提供一个有用的范例。
