Speaker
Description
Adaptive coupling in networks of interacting nonlinear oscillators has
gained recent attention due to the many applications
both in biological and in artificial neural networks, where synaptic
plasticity or adaptive coupling are considered as key
factors in the learning processes. In our studies, we apply adaptive
connectivity rules in exemplary networks consisting
of leaky-integrate-and-fire (LIF) or FitzHugh-Nagumo (FHN) oscillators.
For such networks, in the absence of adaptivity
(i.e., for constant network connectivity), hybrid synchronization
patterns (solitaries, chimeras and bump states) have
been observed [1]. When the coupling strengths get modified, influenced
by the nodal state variables (nodal potentials),
then the network dynamics undergoes structural transitions crossing
domains of different complexity/synchrony [2-3].
Coupling adaptivity (plasticity) may be realized via Hebbian learning
adjusted by the Oja rule (also called 'forgetting' rule)
to prevent the network link weights from growing without bounds. The
resulting adaptive transitions become evident
when the time scales governing the coupling dynamics are much slower
than the ones governing the nodal dynamics
(nodal potentials). Namely, when the coupling time scales are slow, the
network has the time to realize and demonstrate
different synchronization regimes before reaching the final steady
state. The transitions are characterized by abrupt
changes of the average coupling weights and of the Kuramoto order
parameter as the network evolves in time [2-3].
The emergence of adaptive transitions demonstrate how the interplay of
distinct time scales can profoundly influence
the evolution and the collective behavior in dynamical systems.
Literature
[1] Y. Kuramoto and D. Battogtokh
Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase
Oscillators
Nonlinear Phenomena in Complex Systems 5 380 (2002)
http://www.j-npcs.org/online/vol2002/v5no4/v5no4p380.pdf
[2]. A. Provata, G. C. Boulougouris and J. Hizanidis
Adaptive transitions in FitzHugh-Nagumo networks with Hebb-Oja coupling
rules
Journal of Statistical Mechanics: Theory and Experiment, Volume 2026,
044004 (2026)
https://doi.org/10.1088/1742-5468/ae5c93
[3]. A. Provata, G. C. Boulougouris and J. Hizanidis
Synchronization transitions in spiking networks with adaptive coupling
Chaos, Solitons & Fractals, Volume 200, 117128 (2025)
https://doi.org/10.1016/j.chaos.2025.117128