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In this work, we study the dynamical robustness in a system consisting of both active and inactive oscillators. We analytically show that the dynamical robustness of such system is determined by the cross link density between active and inactive subpopulations, which depends on the specific process of inactivation. It is the multi-valued dependence of the cross link density on the control parameter, i.e., the ratio of inactive oscillators in the system, that leads to the fluctuation of the critical points. We further investigate how different network topologies and inactivation strategies affect the fluctuation. Our results explain why the fluctuation is more obvious in heterogeneous networks than in homogeneous ones, and why the low-degree nodes are crucial in terms of dynamical robustness. The analytical results are supported by numerical verifications.
The controllability of synchronization is an intriguing question in complex systems, in which hiearchically-organized heterogeneous elements have asymmetric and activity-dependent couplings. In this study, we introduce a simple and effective way to c
We study the primacy in the Bulgarian urban system. Two groups of cities are studied: (i) the whole Bulgaria city system that contains about 250 cities and is studied in the time interval between 2004 and 2011; and (ii) A system of 33 cities, studied
We report the emergence of stable amplitude chimeras and chimera death in a two-layer network where one layer has an ensemble of identical nonlinear oscillators interacting directly through local coupling and indirectly through dynamic agents that fo
We investigate numerically the clustering behavior of a system of phase oscillators with positive and negative couplings under a periodic external driving field with a bimodal distribution of driving phases. The phase distribution and the mean speed
Many physical, chemical and biological systems exhibit a cooperative or sigmoidal response with respect to the input. In biochemistry, such behavior is called an allosteric effect. Here we demonstrate that a system with such properties can be used to