Vortex merging, oscillation, and quasiperiodic structure in a linear array of elongated vortices

Fukuta, Hiroaki; Murakami, Youichi

doi:10.1103/physreve.57.449

Cited by 18 publications

(11 citation statements)

References 20 publications

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“…The SL system is related not only to the Ginzburg-Landau equation but also describes the general two-dimensional solution of the Navier-Stokes equations [28,29], and thus this model applies to wide variety of situations. In addition, the sign of the phase velocity can be of relevance in several instances such as cyclic flows in plasma [30], atmospheric and oceanic currents [31], and biological media [32]. In such cases the interaction of units with oscillations in the same or opposite directions can be of relevance [33][34][35].…”

Section: Discussionmentioning

confidence: 99%

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Dynamical effects of breaking rotational symmetry in counter-rotating Stuart-Landau oscillators

et al. 2018

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Stuart-Landau oscillators can be coupled so as to either preserve or destroy the rotational symmetry that the uncoupled system possesses. We examine some of the simplest cases of such couplings for a system of two nonidentical oscillators. When the coupling breaks the rotational invariance, there is a qualitative difference between oscillators wherein the phase velocity has the same sign (termed co-rotation) or opposite signs (termed counter-rotation). In the regime of oscillation death the relative sense of the phase rotations plays a major role. In particular, when rotational invariance is broken, counter-rotation or phase velocities of opposite signs appear to destabilize existing fixed points, thereby preserving and possibly extending the range of oscillatory behavior. The dynamical "frustration" induced by counter-rotations can thus suppress oscillation quenching when coupling breaks the symmetry.

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Section: Discussionmentioning

confidence: 99%

“…(22)] and real part of the eigenvalues, Eq. (25) and (31) are shown in Fig. 8 for the two cases of (1) co-rotating oscillators and (2) counter-rotating oscillators.…”

Section: B Symmetry-breaking Casesmentioning

confidence: 99%

Dynamical effects of breaking rotational symmetry in counter-rotating Stuart-Landau oscillators

et al. 2018

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“…In particular, coexisting co-rotating and counter-rotating systems characterized by positive and negative frequencies, respectively, are wide spread in nature. For instance, counter-rotating spirals are observed in protoplasm of the Physarum plasmodium [27], counter-rotating vortices are inevitable in the atmosphere and ocean [28][29][30], in magnetohydrodynamics of plasma flow [31], Bose-Einstein condensates [32,33], and in other physical systems [34][35][36]. Very recently, the counter-rotating frequency induced dynamical effects were also reported in the coupled Stuart-Landau oscillator with symmetry preserving as well as symmetry breaking couplings [37].…”

Section: Modelmentioning

confidence: 97%

Generalization of the Kuramoto model to the Winfree model by a symmetry breaking coupling

M.¹,

Gupta²,

V.³

et al. 2023

Preprint

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We construct a nontrivial generalization of the paradigmatic Kuramoto model by using an additional coupling term that explicitly breaks its rotational symmetry resulting in a variant of the Winfree Model. Consequently, we observe the characteristic features of the phase diagrams of both the Kuramoto model and the Winfree model depending on the degree of the symmetry breaking coupling strength for unimodal frequency distribution. The phase diagrams of both the Kuramoto and the Winfree models resemble each other for symmetric bimodal frequency distribution for a range of the symmetry breaking coupling strength except for region shift and difference in the degree of spread of the macroscopic dynamical states and bistable regions. The dynamical transitions in the bistable states are characterized by an abrupt (first-order) transition in both the forward and reverse traces. For asymmetric bimodal frequency distribution, the onset of bistable regions depends on the degree of the asymmetry. Large degree of the symmetry breaking coupling strength promotes the synchronized stationary state, while a large degree of heterogeneity, proportional to the separation between the two central frequencies, facilitates the spread of the incoherent and standing wave states in the phase diagram for a low strength of the symmetry breaking coupling. We deduce the low-dimensional equations of motion for the complex order parameters using the Ott-Antonsen ansatz for both unimodal and bimodal frequency distributions. We also deduce the Hopf, pitchfork, and saddle-node bifurcation curves from the evolution equations for the complex order parameters mediating the dynamical transitions. Simulation results of the original discrete set of equations of the generalized Kuramoto model agree well with the analytical bifurcation curves.

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“…On the other hand, coexisting co-and counter-rotating dynamical activity has a wide range of applications in diverse fields, including physical [30,31], biological [32,33], and fluid dynamics [34][35][36] contexts. For instance, counter-rotating spirals can be found in biological media, such as Physarum plasmodium protoplasm [32,33].…”

Section: Introductionmentioning

confidence: 99%

Emerging chimera states under non-identical counter-rotating oscillators

Sathiyadevi,

Chandrasekar,

Lakshmanan

2022

Preprint

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Frequency plays a crucial role in exhibiting various collective dynamics in the coexisting co-and counter-rotating systems. To illustrate the impact of counter-rotating frequencies, we consider a network of non-identical and globally coupled Stuart-Landau oscillators with additional perturbation. Primarily, we investigate the dynamical transitions in the absence of perturbation, demonstrating that the transition from desynchronized state to cluster oscillatory state occurs through an interesting partial synchronization state in the oscillatory regime. Followed by this, the system dynamics transits to amplitude death and oscillation death states. Importantly, we find that the observed dynamical states do not preserve the parity(P ) symmetry in the absence of perturbation. When the perturbation is increased one can note that the system dynamics exhibits a new kind of transition which corresponds to a change from incoherent mixed synchronization to coherent mixed synchronization through chimera state. In particular, incoherent mixed synchronization and coherent mixed synchronization states completely preserve the P -symmetry, whereas the chimera state preserves the P -symmetry only partially. To demonstrate the occurrence of such partial symmetry breaking (chimera) state, we use basin stability analysis and discover that partial symmetry breaking exists as a result of the coexistence of symmetry preserving and symmetry breaking behavior in the initial state space. Further, a measure of the strength of P -symmetry is established to quantify the P -symmetry in the observed dynamical states. Subsequently, the dynamical transitions are investigated in the parametric spaces. Finally, by increasing the network size, the robustness of the chimera state is also inspected and we find that the chimera state is robust even in networks of larger sizes. We also show the generality of the above results in the related phase reduced model as well as in other coupled models such as the globally coupled van der Pol and Rössler oscillators.

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Vortex merging, oscillation, and quasiperiodic structure in a linear array of elongated vortices

Cited by 18 publications

References 20 publications

Dynamical effects of breaking rotational symmetry in counter-rotating Stuart-Landau oscillators

Dynamical effects of breaking rotational symmetry in counter-rotating Stuart-Landau oscillators

Generalization of the Kuramoto model to the Winfree model by a symmetry breaking coupling

Emerging chimera states under non-identical counter-rotating oscillators

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