Dynamics of phase oscillator networks with synaptic weight and structural plasticity

Abstract

We study the dynamics of Kuramoto oscillator networks with two distinct adaptation processes, one varying the coupling strengths and the other altering the network structure. Such systems model certain networks of oscillatory neurons where the neuronal dynamics, synaptic weights, and network structure interact with and shape each other. We model synaptic weight adaptation with spike-timing-dependent plasticity (STDP) that runs on a longer time scale than neuronal spiking. Structural changes that include addition and elimination of contacts occur at yet a longer time scale than the weight adaptations. First, we study the steady-state dynamics of Kuramoto networks that are bistable and can settle in synchronized or desynchronized states. To compare the impact of adding structural plasticity, we contrast the network with only STDP to one with a combination of STDP and structural plasticity. We show that the inclusion of structural plasticity optimizes the synchronized state of a network by allowing for synchronization with fewer links than a network with STDP alone. With non-identical units in the network, the addition of structural plasticity leads to the emergence of correlations between the oscillators’ natural frequencies and node degrees. In the desynchronized regime, the structural plasticity decreases the number of contacts, leading to a sparse network. In this way, adding structural plasticity strengthens both synchronized and desynchronized states of a network. Second, we use desynchronizing coordinated reset stimulation and synchronizing periodic stimulation to induce desynchronized and synchronized states, respectively. Our findings indicate that a network with a combination of STDP and structural plasticity may require stronger and longer stimulation to switch between the states than a network with STDP only.

Timing to be precise? An overview of spike timing-dependent plasticity, brain rhythmicity, and glial cells interplay within neuronal circuits

“…Based on these findings of brain rhythms and STDP interactions, it is tempting to propose that STDP occurring at key synapses of a neuronal ensemble will strengthen or weaken (by t-LTP or t-LTD, respectively) the neuronal contribution and their engagement (spike-phase-locking, rhythmic synaptic transmission) to the rhythm generated within the network. This could impact the computational ability of the involved neuronal network, probably serving homeostatic mechanisms with cognitive consequences [ 169 ], as has been observed in computational models [ 170 ]. In addition, these findings support the design of experimental protocols mimicking STDP and rhythm interactions [ 38 , 113 , 137 ] and that STDP can modify circuitry properties and vice-versa.…”

Perspectives on adaptive dynamical systems

“…• Different plasticity mechanisms: In Parkinson's disease pathophysiology, both spike-timing-dependent plasticity and structural plasticity 281,282 are important 269 and may induce different stimulation responses. 283,284 These computationally derived predictions and results enabled to design appropriate protocols for pre-clinical and clinical studies.…”

Synchronization in STDP-driven memristive neural networks with time-varying topology

“…The issues of synchronization phenomena in networks undergoing two adaptive processes have not received sufficient research attention. In one study, published in [51], the authors examined this problem by analyzing Kuramoto oscillator networks that undergo two adaptation processes: one that modifies coupling strengths and another that changes the network structure by pruning existing synaptic contacts and adding new ones. By comparing networks with only STDP to those with both STDP and structural plasticity, the authors assessed the effects of structural plasticity and found that it enhances the synchronized state of a network.…”