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

Punetha, Nirmal; Varshney, Vaibhav; Sahoo, Samir; Saxena, Garima; Prasad, Awadhesh; Ramaswamy, Ramakrishna

doi:10.1103/physreve.98.022212

Cited by 13 publications

(5 citation statements)

References 55 publications

(54 reference statements)

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“…Stuart-Landau limit cycle oscillator is a general, paradigmatic model, which can be used to model a variety of nonlinear dynamical systems near the Hopf bifurcation point [41,42,43,44]. We consider a one-dimensional ring network of coupled Stuart-Landau oscillators and investigate its dynamical behavior by including a repulsive link along with a symmetry breaking coupling.…”

Section: The Modelmentioning

confidence: 99%

Long-range interaction induced collective dynamical behaviors

Sathiyadevi¹,

Chandrasekar²,

Senthilkumar³

et al. 2019

J. Phys. A: Math. Theor.

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Long-range interacting systems are omnipresent in nature. We investigate here the collective dynamical behavior in a long-range interacting system consisting of coupled Stuart-Landau limit cycle oscillators. In particular, we analyze the impact of a repulsive coupling along with a symmetry breaking coupling. We report that the addition of repulsive coupling of sufficient strength can induce a swing of the synchronized state which will start disappearing with increasing disorder as a function of the repulsive coupling. We also deduce analytical stability conditions for the oscillatory states including synchronized state, solitary state, two-cluster state as well as oscillation death state. Finally, we have also analyzed the effect of power-law exponent on the observed dynamical states.

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Section: The Modelmentioning

confidence: 99%

Long-range interaction induced collective dynamical behaviors

Sathiyadevi¹,

Chandrasekar²,

Senthilkumar³

et al. 2019

J. Phys. A: Math. Theor.

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“…Recent theoretical progress has tended to concentrate on particular aspects of coupling functions, with some being more focused on the overall interactions or qualitative states, while others study unique characteristics of coupling functions and how they affect the overall interactions [10][11][12][13][14][15][16]. In this way, the coupling functions play important roles in the phenomena and the qualitative states resulting from the interactions.…”

Section: Recent Work On Coupling Functionsmentioning

confidence: 99%

Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

Stankovski

Pereira

McClintock

et al. 2019

Phil. Trans. R. Soc. A.

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Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterized by coupling functions—which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarizes earlier work on coupling functions, reviews recent developments, presents the state of the art, and looks forward to guide the future evolution of the field.This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

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“…Later, the realizations of mixed synchronization were also revealed in both experimental and theoreti-cal systems [43]. Further, the breaking of rotational symmetry induced dynamical effects were investigated in counter-rotating oscillators with symmetry preserving and symmetry breaking couplings [44]. Recently, the aging transitions have also been investigated in counterrotating oscillators [45].…”

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

Cited by 13 publications

References 55 publications

Long-range interaction induced collective dynamical behaviors

Long-range interaction induced collective dynamical behaviors

Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

Emerging chimera states under non-identical counter-rotating oscillators

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