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DDC: 530 × Subject: Synchronization ×

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Now showing 1 - 4 of 4
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    General scaling of maximum degree of synchronization in noisy complex networks
    (Bristol : Institute of Physics Publishing, 2014) Traxl, D.; Boers, N.; Kurths, J.
    The effects of white noise and global coupling strength on the maximum degree of synchronization in complex networks are explored. We perform numerical simulations of generic oscillator models with both linear and non-linear coupling functions on a broad spectrum of network topologies. The oscillator models include the Fitzhugh-Nagumo model, the Izhikevich model and the Kuramoto phase oscillator model. The network topologies range from regular, random and highly modular networks to scale-free and small-world networks, with both directed and undirected edges. We then study the dependency of the maximum degree of synchronization on the global coupling strength and the noise intensity. We find a general scaling of the synchronizability, and quantify its validity by fitting a regression model to the numerical data.
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    Cartesian product of synchronization transitions and hysteresis
    (Bristol : Institute of Physics Publishing, 2017) Wang, C.; Zou, Y.; Guan, S.; Kurths, J.
    We present theoretical results when applying the Cartesian product of two Kuramoto models on different network topologies. By a detailed mathematical analysis, we prove that the dynamics on the Cartesian product graph can be described by the canonical equations as the Kuramoto model. We show that the order parameter of the Cartesian product is the product of the order parameters of the factors. On the product graph, we observe either continuous or discontinuous synchronization transitions. In addition, under certain conditions, the transition from an initially incoherent state to a coherent one is discontinuous, while the transition from a coherent state to an incoherent one is continuous, presenting a mixture state of first and second order synchronization transitions. Our numerical results are in a good agreement with the theoretical predictions. These results provide new insight for network design and synchronization control.
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    Adaptive elimination of synchronization in coupled oscillator
    (Bristol : Institute of Physics Publishing, 2017) Zhou, S.; Ji, P.; Zhou, Q.; Feng, J.; Kurths, J.; Lin, W.
    We present here an adaptive control scheme with a feedback delay to achieve elimination of synchronization in a large population of coupled and synchronized oscillators. We validate the feasibility of this scheme not only in the coupled Kuramoto's oscillators with a unimodal or bimodal distribution of natural frequency, but also in two representative models of neuronal networks, namely, the FitzHugh-Nagumo spiking oscillators and the Hindmarsh-Rose bursting oscillators. More significantly, we analytically illustrate the feasibility of the proposed scheme with a feedback delay and reveal how the exact topological form of the bimodal natural frequency distribution influences the scheme performance. We anticipate that our developed scheme will deepen the understanding and refinement of those controllers, e.g. techniques of deep brain stimulation, which have been implemented in remedying some synchronization-induced mental disorders including Parkinson disease and epilepsy.
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    Recovery time after localized perturbations in complex dynamical networks
    (Bristol : Institute of Physics Publishing, 2017) Mitra, C.; Kittel, T.; Choudhary, A.; Kurths, J.; Donner, R.V.
    Maintaining the synchronous motion of dynamical systems interacting on complex networks is often critical to their functionality. However, real-world networked dynamical systems operating synchronously are prone to random perturbations driving the system to arbitrary states within the corresponding basin of attraction, thereby leading to epochs of desynchronized dynamics with a priori unknown durations. Thus, it is highly relevant to have an estimate of the duration of such transient phases before the system returns to synchrony, following a random perturbation to the dynamical state of any particular node of the network. We address this issue here by proposing the framework of single-node recovery time (SNRT) which provides an estimate of the relative time scales underlying the transient dynamics of the nodes of a network during its restoration to synchrony. We utilize this in differentiating the particularly slow nodes of the network from the relatively fast nodes, thus identifying the critical nodes which when perturbed lead to significantly enlarged recovery time of the system before resuming synchronized operation. Further, we reveal explicit relationships between the SNRT values of a network, and its global relaxation time when starting all the nodes from random initial conditions. Earlier work on relaxation time generally focused on investigating its dependence on macroscopic topological properties of the respective network. However, we employ the proposed concept for deducing microscopic relationships between topological features of nodes and their respective SNRT values. The framework of SNRT is further extended to a measure of resilience of the different nodes of a networked dynamical system. We demonstrate the potential of SNRT in networks of Rössler oscillators on paradigmatic topologies and a model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics illustrating the conceivable practical applicability of the proposed concept.