Dynamics of Random Neural Networks with Bistable Units

Abstract

We construct and analyze a rate-based neural network model in which self-interacting units represent clusters of neurons with strong local connectivity and random inter-unit connections reflect long-range interactions. When sufficiently strong, the self-interactions make the individual units bistable. Simulation results, mean-field calculations and stability analysis reveal the different dynamic regimes of this network and identify the locations in parameter space of its phase transitions. We identify an interesting dynamical regime exhibiting transient but long-lived chaotic activity that combines features of chaotic and multiple fixed-point attractors.

References in corpus (1)

• Properties of networks with partially structured and partially random connectivity

Cited by in corpus (39)

• Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation
• Intrinsically-generated fluctuating activity in excitatory-inhibitory networks
• Correlations between synapses in pairs of neurons slow down dynamics in randomly connected neural networks
• Path Integral Approach to Random Neural Networks
• Local Dynamics in Trained Recurrent Neural Networks
• Coherent Ising machines -- Quantum optics and neural network perspectives
• Linking structure and activity in nonlinear spiking networks
• Edge of chaos and avalanches in neural networks with heavy-tailed synaptic weight distribution
• Shaping neural circuits by high order synaptic interactions
• Neural Field Models: A mathematical overview and unifying framework
• Synchronization of two memristive coupled van der Pol oscillators
• How single neuron properties shape chaotic dynamics and signal transmission in random neural networks
• Dimension of activity in random neural networks
• Does the brain behave like a (complex) network? I. Dynamics
• Contrasting the effects of adaptation and synaptic filtering on the timescales of dynamics in recurrent networks
• Integration of continuous-time dynamics in a spiking neural network simulator
• Generalized network density matrices for analysis of multiscale functional diversity
• On the number of limit cycles in asymmetric neural networks
• Multiplexing-based control of stochastic resonance
• Large Deviations Approach to Random Recurrent Neuronal Networks: Parameter Inference and Fluctuation-Induced Transitions
• Extended Anderson Criticality in Heavy-Tailed Neural Networks
• Consequences of Dale's law on the stability-complexity relationship of random neural networks
• Input correlations impede suppression of chaos and learning in balanced rate networks
• Two-color optically-addressed spatial light modulator as generic spatio-temporal systems
• The coherent Ising machine with quantum feedback: the total and conditional master equation methods
• On the number of limit cycles in diluted neural networks
• Unlearnable Games and "Satisficing'' Decisions: A Simple Model for a Complex World
• Drive-specific adaptation in disordered mechanical networks of bistable springs
• Impact of membrane bistability on dynamical response of neuronal populations
• Gating creates slow modes and controls phase-space complexity in GRUs and LSTMs
• Kinetic Ising Models with Self-interaction: Sequential and Parallel Updating
• Multiplexing-based control of wavefront propagation: the interplay of inter-layer coupling, asymmetry and noise
• Effect of Synaptic Heterogeneity on Neuronal Coordination
• Spontaneous and stimulus-induced coherent states of critically balanced neuronal networks
• Basins of Attraction: A Dynamical Zoo
• Classes of non-Gaussian random matrices: long-range eigenvalue correlations and non-ergodic extended eigenvectors
• Bifurcations of a neural network model with symmetry
• Continuous parameter working memory in a balanced chaotic neural network
• Chaos-guided Input Structuring for Improved Learning in Recurrent Neural Networks