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Register a new userFluctuation of Dynamical Robustness in a Networked Oscillators System
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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.
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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 control synchronization in such a complex system by changing the complexity of subsystems. We consider three Stuart-Landau oscillators as a minimal subsystem for generating various complexity, and hiearchically connect the subsystems through a mean field of their activities. Depending on the coupling signs between three oscillators, subsystems can generate ample dynamics, in which the number of attractors specify their complexity. The degree of synchronization between subsystems is then controllable by changing the complexity of subsystems. This controllable synchronization can be applied to understand the synchronization behavior of complex biological networks.
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 over the time interval 1887 till 2010. For these cities the 1946 population was over $10 000$ inhabitants. The notion of primacy in the two systems of cities is studied first from the global primacy index of Sheppard [$^1$]. Several (new) additional indices are introduced in order to compensate defects in the Sheppard index. Numerical illustrations are illuminating through the so called length ratio.
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 form the second layer. The nonlocality in the interaction among the dynamical agents in the second layer induces different types of chimera related dynamical states in the first layer. The amplitude chimeras developed in them are found to be extremely stable, while chimera death states are prevalent for increased coupling strengths. The results presented are for a system of coupled Stuart-Landau oscillators and can in general represent systems with short-range interactions coupled to another set of systems with long range interactions. In this case, by tuning the range of interactions among the oscillators or the coupling strength between the two types of systems, we can control the nature of chimera states and the system can be restored to homogeneous steady states. The dynamic agents interacting nonlocally with long-range interactions can be considered as a dynamic environment or medium interacting with the system. We indicate how the second layer can act as a reinforcement mechanism on the first layer under various possible interactions for desirable effects.
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 of the traveling state, as well as the order parameter for synchronization, are computed as the driving amplitude is varied. We observe that the periodically-driven system can also host traveling states for parameters in the same range as those for the case of a system without a driving field. The traveling speed is found to depend non-monotonically on the driving amplitude. In particular, oscillators divide into four clusters and move in pairs. Further, depending on the driving amplitude, two kinds of traveling mode arise: pairs of clusters traveling in the same direction (symmetric mode) and in opposite directions (antisymmetric mode). In the latter case (antisymmetric traveling mode), the average phase speed of the whole system apparently vanishes. A phenomenological argument for such behavior is given.
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 discriminate the amplitude or frequency of an external periodic perturbation or input. Numerical simulations performed for a model sigmoidal kinetics illustrate that there exists a narrow range of frequencies and amplitudes within which the system evolves toward significantly different states. Therefore, observation of system evolution should provide information about the characteristics of the perturbation. The discrimination properties for periodic perturbation are generic. They can be observed in various dynamical systems and for different types of periodic perturbation. end{abstract}
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