Asymmetric adaptivity induces recurrent synchronization in complex networks

Thiele, Max; Berner, Rico; Tass, Peter A.; Schöll, Eckehard; Yanchuk, Serhiy

doi:10.1063/5.0128102

Cited by 19 publications

(7 citation statements)

References 73 publications

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“…For such adaptation, the network naturally forms clusters of strongly connected units (see Figure 3). By contrast, the causality of traditional asymmetric STDP rules will be reflected in the network structure as shown in Figure 5 and highlighted very recently in Thiele et al (2023). To analyze the mean-field dynamics of such networks, a natural approach would be to computationally identify emerging feedforward structures in such networks instead of looking for clusters.…”

Section: Discussionmentioning

confidence: 99%

Mean-Field Approximations With Adaptive Coupling for Networks With Spike-Timing-Dependent Plasticity

Duchet,

Bick,

Byrne

2023

Neural Computation

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Understanding the effect of spike-timing-dependent plasticity (STDP) is key to elucidating how neural networks change over long timescales and to design interventions aimed at modulating such networks in neurological disorders. However, progress is restricted by the significant computational cost associated with simulating neural network models with STDP and by the lack of low-dimensional description that could provide analytical insights. Phase-difference-dependent plasticity (PDDP) rules approximate STDP in phase oscillator networks, which prescribe synaptic changes based on phase differences of neuron pairs rather than differences in spike timing. Here we construct mean-field approximations for phase oscillator networks with STDP to describe part of the phase space for this very high-dimensional system. We first show that single-harmonic PDDP rules can approximate a simple form of symmetric STDP, while multiharmonic rules are required to accurately approximate causal STDP. We then derive exact expressions for the evolution of the average PDDP coupling weight in terms of network synchrony. For adaptive networks of Kuramoto oscillators that form clusters, we formulate a family of low-dimensional descriptions based on the mean-field dynamics of each cluster and average coupling weights between and within clusters. Finally, we show that such a two-cluster mean-field model can be fitted to synthetic data to provide a low-dimensional approximation of a full adaptive network with symmetric STDP. Our framework represents a step toward a low-dimensional description of adaptive networks with STDP and could, for example inform the development of new therapies aimed at maximizing the long-lasting effects of brain stimulation.

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Section: Discussionmentioning

confidence: 99%

Mean-Field Approximations With Adaptive Coupling for Networks With Spike-Timing-Dependent Plasticity

Duchet,

Bick,

Byrne

2023

Neural Computation

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show abstract

“…By contrast, the causality of traditional asymmetric STDP rules will be reflected in the network structure as shown in Fig. 5 and highlighted very recently in (Thiele, Berner, Tass, Schöll, & Yanchuk, 2023). To analyze the mean-field dynamics of such networks, a natural approach would be to computationally identify emerging feed-forward structures in such networks instead of looking for clusters.…”

Section: Discussionmentioning

confidence: 99%

Mean-field approximations with adaptive coupling for networks with spike-timing-dependent plasticity

Duchet

Bick

Byrne

2022

Preprint

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Understanding the effect of spike-timing-dependent plasticity (STDP) is key to elucidate how neural networks change over long timescales and to design interventions aimed at modulating such networks in neurological disorders. However, progress is restricted by the significant computational cost associated with simulating neural network models with STDP, and by the lack of low-dimensional description that could provide analytical insights. To approximate STDP in phase oscillator networks, simpler phase-difference-dependent plasticity (PDDP) rules have been developed, which prescribe synaptic changes based on phase differences of neuron pairs rather than differences in spike timing. Here we construct mean-field approximations for phase oscillator networks with STDP to describe the dynamics of large networks of adaptive oscillators. We first show that single-harmonic PDDP rules can approximate a simple form of symmetric STDP, while multi-harmonic rules are required to accurately approximate causal STDP. We then derive exact expressions for the evolution of the average PDDP coupling weight in terms of network synchrony. For adaptive networks of Kuramoto oscillators that form clusters, we formulate a low-dimensional description based on mean field dynamics and average coupling weight. Finally, we show that such a two-cluster mean-field model can be fitted to provide a low-dimensional approximation of a full adaptive network with symmetric STDP. Our framework represents a step towards a low-dimensional description of adaptive networks with STDP, and could for example inform the development of new therapies aimed at maximizing the long-lasting effects of brain stimulation.

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“…In the phase-locked regime, the dynamics relax instantaneously to equilibrium, which defines the critical manifold of the slow-fast system on which A i takes its value at equilibrium. In the regime where the phase difference ϕ ( t ) is drifting, we replace the instantaneous frequency in A i by the temporal average Ω i ; this is similar to the approach in [15]. Finally, we consider the system at the border between the two regimes.…”

Section: Coupling Heterodimer Dynamics With Oscillatory Activitymentioning

confidence: 99%

“…Networks exhibiting such mutual interactions between dynamical processes and network topology are referred to as adaptive, or coevolutionary, networks [6, 10, 11]. In a range of applications, including oscillator networks [12–15], consensus dynamics [16], and epidemic-resource dynamics [17], coevolutionary dynamics may also operate on disparate timescales. Although techniques from geometric singular perturbation theory [18] and averaging theory [19] can provide insights into the emerging multiple-timescale dynamics, these methods become daunting in high dimensions.…”

Section: Introductionmentioning

confidence: 99%

Neuronal activity induces symmetry breaking in neurodegenerative disease spreading

Alexandersen,

Goriely,

Bick

2023

Preprint

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Dynamical systems on networks typically involve several dynamical processes evolving at different timescales. For instance, in Alzheimer’s disease, the spread of toxic protein throughout the brain not only disrupts neuronal activity but is also influenced by neuronal activity itself, establishing a feed-back loop between the fast neuronal activity and the slow protein spreading. Motivated by the case of Alzheimer’s disease, we study the multiple-timescale dynamics of a heterodimer spreading process on an adaptive network of Kuramoto oscillators. Using a minimal two-node model, we establish that heterogeneous oscillatory activity facilitates toxic outbreaks and induces symmetry breaking in the spreading patterns. We then extend the model formulation to larger networks and perform numerical simulations of the slow-fast dynamics on common network motifs and on the brain connectome. The simulations corroborate the findings from the minimal model, underscoring the significance of multiple-timescale dynamics in the modeling of neurodegenerative diseases.

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Asymmetric adaptivity induces recurrent synchronization in complex networks

Cited by 19 publications

References 73 publications

Mean-Field Approximations With Adaptive Coupling for Networks With Spike-Timing-Dependent Plasticity

Mean-Field Approximations With Adaptive Coupling for Networks With Spike-Timing-Dependent Plasticity

Mean-field approximations with adaptive coupling for networks with spike-timing-dependent plasticity

Neuronal activity induces symmetry breaking in neurodegenerative disease spreading

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