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    Frustration-induced collective dynamical states in pulse-coupled adaptive Winfree networks

    R. Anand*, V. K. Chandrasekar†, and R. Suresh‡

    • Centre for Nonlinear Science and Engineering, Department of Physics, School of EEE, SASTRA Deemed to be University, Thanjavur, Tamil Nadu 613401, India

    • *Contact author: anand19032002@gmail.com
    • †Contact author: chandrasekar@eee.sastra.edu
    • ‡Contact author: suresh@eee.sastra.edu

    Phys. Rev. E 114, 014201 – Published 1 July, 2026

    DOI: https://doi.org/10.1103/zt8w-4bg3

    Abstract

    We investigate collective dynamics in a pulse-coupled adaptive Winfree network under the influence of a frustration (phase-lag) parameter. The coupling strengths coevolve according to a Hebbian adaptation rule and self-organize to support a wide variety of collective states. We observe frequency-clustered states, entrainment, bump states, bump-frequency cluster states, antipodal and multiantipodal cluster states, chimera states, and incoherent dynamics. Notably, we report the spontaneous emergence of entrainment, bump, and bump-frequency cluster states in an adaptive network without any external forcing. To systematically characterize these regimes, we introduce three complementary measures of incoherence based on (i) time-averaged frequencies, (ii) instantaneous phases, and (iii) mean frequencies per bin. These measures enable the construction of one- and two-parameter phase diagrams that clearly delineate transitions between distinct dynamical states. Furthermore, we analytically derive the stability condition for the frequency-entrained state, which shows excellent agreement with numerical simulations. Our results highlight the crucial role of frustration-mediated plasticity in shaping rich self-organized dynamics in pulse-coupled adaptive networks.

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