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Language: search.filters.language.English (United States)Subject: search.filters.subject.Nonlinear Sciences - Adaptation and Self-Organizing Systems

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    On numerical solutions of linear fractional differential equations
    (2021)
    Seferi, Ylldrita
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    Fractional differential equations have excited considerable interest recently, both in pure and applied mathematics. In this paper, we apply Fractional Adams-Bashforth Method (FAB), Fractional Adams-Bashforth-Moulton Method (FABM) and Fractional Multistep Differential Transform Method (FMDTM), for obtaining the numerical solutions of two distinct linear systems of fractional differential equations with fractional derivatives described in the Caputo sense. The numerical results for the three methods are compared with the exact solution for each linear system by using the relative difference between the exact and the approximate solution at each integration point. The results are given both graphically and tabularly, concluding that, aside from occasional non-monotoncity for small time values, all three numerical methods gradually diverge from the exact solution with increasing integration time, and the superiority of each numerical method over the others depends on the particular system under investigation.
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    Amplitude death and chimera patterns in complex networks with time delays
    (Russian Academy of Sciences, Institute of Applied Physics, Nizhny Novgorod, 2017)
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    Schöll, Eckehard
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    Zakharova, Anna
    We study the conditions of amplitude death in a network of delay-coupled limit cycle oscillators with time-varying delay coupling. By generalizing the master stability function formalism, we analyze the amplitude death regimes in a ring and a multiplex network of Stuart-Landau oscillators. We further investigate the influence of time delay (constant, time-varying, or distributed) on the dynamical regimes and the lifetime of amplitude chimera states in the case when coupling breaks the rotational S1 symmetry. We demonstrate that the lifetime of amplitude chimeras and related incoherent states can be deliberately reduced or increased, depending upon the type of coupling delay.
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    Control of amplitude chimeras by time delay in dynamical networks
    (The European Nonlinear Dynamics Conference (ENOC), Congressline Ltd., Budapest, 2017)
    Schöll, Eckehard
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    Zakharova, Anna
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    We investigate the influence of time-delayed coupling in a ring network of non-locally coupled Stuart-Landau oscillators upon chimera states, i.e., space-time patterns with coexisting partially coherent and partially incoherent domains. We focus on amplitude chimeras which exhibit incoherent behavior with respect to the amplitude rather than the phase and are transient patterns, and show that their lifetime can be significantly enhanced by coupling delay. To characterize their transition to phase-lag synchronization (coherent traveling waves) and other coherent structures, we generalize the Kuramoto order parameter. Contrasting the results for instantaneous coupling with those for constant and for time-varying coupling delays, we demonstrate that the lifetime of amplitude chimera states and related partially incoherent states can be controlled, i.e., deliberately reduced or increased, depending upon the type of coupling delay.