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Exotic states induced by coevolving connection weights and phases in complex networks

S. Thamizharasan1, V. K. Chandrasekar2,*, M. Senthilvelan1, Rico Berner3,4, Eckehard Schöll3,5,6, and D. V. Senthilkumar7,†

  • 1Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli-620 024, Tamil Nadu, India
  • 2Centre for Nonlinear Science & Engineering, Department of Physics, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur-613 401, Tamil Nadu, India
  • 3Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
  • 4Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
  • 5Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, 14473 Potsdam, Germany
  • 6Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, Philippstraße 13, 10115 Berlin, Germany
  • 7School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram-695 551, Kerala, India

  • *chandru25nld@gmail.com
  • †skumar@iisertvm.ac.in
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Phys. Rev. E 105, 034312 – Published 28 March, 2022

DOI: https://doi.org/10.1103/PhysRevE.105.034312

Abstract

We consider an adaptive network, whose connection weights coevolve in congruence with the dynamical states of the local nodes that are under the influence of an external stimulus. The adaptive dynamical system mimics the adaptive synaptic connections common in neuronal networks. The adaptive network under external forcing displays exotic dynamical states such as itinerant chimeras whose population density of coherent and incoherent domains coevolves with the synaptic connection, bump states, and bump frequency cluster states, which do not exist in adaptive networks without forcing. In addition, the adaptive network also exhibits partial synchronization patterns such as phase and frequency clusters, forced entrained, and incoherent states. We introduce two measures for the strength of incoherence based on the standard deviation of the temporally averaged (mean) frequency and on the mean frequency to classify the emergent dynamical states as well as their transitions. We provide a two-parameter phase diagram showing the wealth of dynamical states. We additionally deduce the stability condition for the frequency-entrained state. We use the paradigmatic Kuramoto model of phase oscillators, which is a simple generic model that has been widely employed in unraveling a plethora of cooperative phenomena in natural and man-made systems.

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Outline

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Phys. Rev. E 105, 034312– Published 28 March, 2022
  • Received 16 November 2021
  • Accepted 7 March 2022
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