Chimera states in Leaky Integrate-and-Fire dynamics with power law coupling

  • PDF / 1,201,282 Bytes
  • 9 Pages / 595.276 x 785.197 pts Page_size
  • 72 Downloads / 173 Views

DOWNLOAD

REPORT


THE EUROPEAN PHYSICAL JOURNAL B

Regular Article

Chimera states in Leaky Integrate-and-Fire dynamics with power law coupling Astero Provata 1,a and Ioannis E. Venetis 2 1

2

Institute of Nanoscience and Nanotechnology, National Center for Scientific Research “Demokritos”, 15341 Athens, Greece Computer Engineering and Informatics Department, University of Patras, Patras, Greece Received 15 May 2020 / Received in final form 2 July 2020 Published online 24 August 2020 c EDP Sciences / Societ`

a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. We investigate the robustness of chimera states under the influence of a nonlinear coupling in the form of a power law with exponent α. Taking as working example the Leaky Integrate-and-Fire model coupled in a 1D ring geometry, we show that the chimera states prevail for large values of the exponent α and small values of the coupling strength, while full synchronization is observed in the opposite ends. Our numerical results indicate that the coupling range R does not influence the frequency of oscillations in the coherent or in the incoherent domains. To the contrary, the R value affects the form of the chimera state: the size of the incoherent domains increase monotonically with R in expense of the size of the coherent ones. As an added value, our numerical results demonstrate that the frequency of oscillations decreases monotonically with the power exponent α. This feature can be useful in controlling the frequency of a network of oscillators by simply varying the nonlinearity exponent in the coupling, without modifying any of the other network attributes or parameters.

1 Introduction Recent numerical and experimental studies in the domain of synchronization of coupled oscillators have revealed the existence of unexpected states consisting of coexisting synchronous and asynchronous elements, which are known as “chimera states”. These states are found in diverse nonlinear oscillatory dynamics and coupling schemes and they even occur in systems of identically linked, identical oscillators [1–4]. Chimera states are mostly investigated in connectivity geometries with exponential, Gaussian, rectangular or hierarchical kernels [1,5–9]. In this study we present first results using power law coupling terms with different exponents, which can be found in many interacting particle systems. We provide numerical evidence that chimera states are also possible for nonlocal, power law coupling schemes and we explore the parameter regions where chimera states are obtained. The first numerical account of a chimera state was reported in a seminal paper by Kuramoto and Battogtokh in 2002 [5] and was also described in the same year in reference [10]. The term “chimera state” was proposed two years later by Abrams and Strogatz [11] to describe the hybrid state consisting of two (or more) different coexisting domains. While in the original studies the Kuramoto a

e-mail: [email protected]

model was used to describe the internal dynamics of th