![]() ![]() ![]() By this time, this phenomenon has been widely explored in single-layer networks (Abrams and Strogatz, 2004 Sethia et al., 2008 Laing, 2009 Hagerstrom et al., 2012 Martens et al., 2013 Omelchenko et al., 2013 Gopal et al., 2014 Hart et al., 2019 Majhi et al., 2019 Parastesh et al., 2020 Wang and Liu, 2020), multilayer networks (Ghosh and Jalan, 2016 Maksimenko et al., 2016 Sawicki et al., 2018 Ruzzene et al., 2020), and 3D networks (Maistrenko et al., 2015 Kasimatis et al., 2018 Kundu et al., 2019) with different forms of chimeras such as traveling chimera (Bera et al., 2016a Omel'chenko, 2019 Dudkowski et al., 2019 Alvarez-Socorro et al., 2021) and spiral chimera (Martens et al., 2010 Gu et al., 2013). Later, it has been established that chimera states are possible stable states (Pecora et al., 2014 Omel'chenko, 2018 Laing, 2019) in an ensemble of identical oscillators and with symmetry in the connectivity matrix or the topology of a network. It is shown that, in the case of three DC electrical machines, these positions influence the time to obtain a synchronous state between the DC electrical machines. Moreover, in the modelling of the system, the positions on the plate occupied by DC electrical machines are taken into account by using the Heaviside function. This has been observed by numerically exploring the dynamics of the system for various possibilities that could occur. It appears that the time delay induces a rapid or late synchronization observed between the DC sources. Great attention is put on the incidence of such study on the vibrations amplitude of the plate, which are considerably reduced in some cases. The existence conditions of the fixed point and the stability conditions are derived and presented. The stability analysis of the whole studied system (with two machines) around the obtained fixed point is done through analytical and numerical approaches by using the generalized Lyapunov and Routh-Hurwitz criterion. The DC electrical machines are considered here as non-ideal oscillators, rotating in the same direction and acting as an external excitation on a specific surface of the plate. ![]() The present paper aims to present the effects of late switching on (time delay) between two or three DC electrical machines characterized by limited power supplies on their fast or late self-synchronization when mounted on a rectangular plate with simply supported edges. Our work explores the criticality in transient behavior as well as the phase transition from chimera to synchronization under increasing perturbation, which may shed new insights to controlling coupled oscillator system with the help of perturbation through inducing phase transition between symmetry and asymmetry self-organized states. Moreover, the comparison between different clusters systems shows that the critical points of odd and even clusters converge in proportional like sequences as the cluster number approaches infinity, implying that this critical behavior can be modeled and enabling the articulation of a phenomenological model. Based on adequate verification, we fit and analyze the distribution of the transient time, and observe power-law variation process as perturbation strengths approaches the critical point, which divided the phase of stable chimera and synchronization states. Through systematic numerical analysis of the evolution of the spatiotemporal pattern of the multi-cluster chimera states, we uncover a critical behavior of the system in transient time towards either chimera or synchronization as the final stable state. While how the system is steering towards different final destinies upon spatially localized perturbation is still unknown. (Color figure online)Ĭhimera states in spatiotemporal dynamical systems have been investigated in physical, chemical, and biological systems. Different types of dynamics of network (1) for varied wheel’s mass M and pendula coupling strength ks\documentclass N/m]. ![]()
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