528 research outputs found

    Synchronization of impulsively coupled complex systems with delay

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    Author name used in this publication: Francis AustinVersion of RecordPublishe

    Some new less conservative criteria for impulsive synchronization of a hyperchaotic Lorenz system based on small impulsive signals

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    In this Letter the issue of impulsive Synchronization of a hyperchaotic Lorenz system is developed. We propose an impulsive synchronization scheme of the hyperchaotic Lorenz system including chaotic systems. Some new and sufficient conditions on varying impulsive distances are established in order to guarantee the synchronizability of the systems using the synchronization method. In particular, some simple conditions are derived for synchronizing the systems by equal impulsive distances. The boundaries of the stable regions are also estimated. Simulation results show the proposed synchronization method to be effective. (C) 2009 Elsevier Ltd. All rights reserved

    Transient and chaotic low-energy transfers in a system with bistable nonlinearity

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    The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to a lightweight mass by means of a spring with both cubic nonlinear and negative linear components is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator, excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics evolves solely in-well. The description of the former dissipative phenomenon is provided in a two-dimensional projection of the phase space, where transitions between in-well and cross-well oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second mechanism is described in terms of secondary limiting phase trajectories of the nonlinear attachment under certain resonance conditions. The analytical treatment of the two aformentioned low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully validate our analytical predictions

    Observer-based Synchronization of Multi-agent Systems Using Intermittent Output Measurements

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    The problem of synchronizing multiple continuous-time linear time-invariant systems connected over a complex network, with intermittently available measurements of their outputs, is considered. To solve this problem, we propose a distributed observer-based feedback controller that utilizes a local hybrid observer to estimate neighboring states only from output measurements at such potentially nonperiodic isolated event times. Due to the inherent continuous and discrete dynamics emerging from coupling the impulsive measurement updates and the interconnected networked systems, we use hybrid systems to model and analyze the resulting closed-loop system. The problem of synchronization and state estimation is then recast as a set stabilization problem, and, utilizing a Lyapunov-based analysis for hybrid systems, we provide sufficient conditions for global exponential stability of the synchronization and zero estimation error set. A numerical example is provided to illustrate the results

    Anti-phase synchronization and symmetry-breaking bifurcation of impulsively coupled oscillators.

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    This paper studies the synchronization in two mechanical oscillators coupled by impacts which can be considered as a class of state-dependent impulsively coupled oscillators. The two identical oscillators are harmonically excited in a counter phase, and the synchronous (anti-phase synchronization) and the asynchronous motions are considered. One- and two-parameter bifurcations of the system have been studied by varying the amplitude and the frequency of external excitation. Numerical simulations show that the system could exhibit complex phenomena, including symmetry and asymmetry periodic solutions, quasi-periodic solutions and chaotic solutions. In particular, the regimes in anti-phase synchronization are identified, and it is found that the symmetry-breaking bifurcation plays an important role in the transition from synchronous to asynchronous motion

    Kick synchronization versus diffusive synchronization

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    The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on synchronization, and the (hybrid) kick model, that accounts for most popular examples of synchronization, but for which only few theoretical results exist. The paper stresses fundamental differences between the two models, such as the different contraction measures underlying the analysis, as well as important analogies that can be drawn in the limit of weak coupling.Peer reviewe
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