Chaos versus noise as drivers of multistability in neural networks

Abstract

The multistable behavior of neural networks is actively being studied as a landmark of ongoing cerebral activity, reported in both functional Magnetic Resonance Imaging (fMRI) and electro- or magnetoencephalography recordings. This consists of a continuous jumping between different partially synchronized states in the absence of external stimuli. It is thought to be an important mechanism for dealing with sensory novelty and to allow for efficient coding of information in an ever-changing surrounding environment. Many advances have been made to understand how network topology, connection delays, and noise can contribute to building this dynamic. Little or no attention, however, has been paid to the difference between local chaotic and stochastic influences on the switching between different network states. Using a conductance-based neural model that can have chaotic dynamics, we showed that a network can show multistable dynamics in a certain range of global connectivity strength and under deterministic conditions. In the present work, we characterize the multistable dynamics when the networks are, in addition to chaotic, subject to ion channel stochasticity in the form of multiplicative (channel) or additive (current) noise. We calculate the Functional Connectivity Dynamics matrix by comparing the Functional Connectivity (FC) matrices that describe the pair-wise phase synchronization in a moving window fashion and performing clustering of FCs. Moderate noise can enhance the multistable behavior that is evoked by chaos, resulting in more heterogeneous synchronization patterns, while more intense noise abolishes multistability. In networks composed of nonchaotic nodes, some noise can induce multistability in an otherwise synchronized, nonchaotic network. Finally, we found the same results regardless of the multiplicative or additive nature of noise.

Cortical ignition dynamics is tightly linked to the core organisation of the human connectome

“…Even if we cannot yet fully explain the observed ignition behaviour of the model in terms of the network organisation of the connectome it embeds, these organisations remain nevertheless a strong determinant of the observed dynamics. This finding is in apparent contrast with theoretical works based on more abstract network topologies [8,9,15] in which the variety of possible dynamical behaviours transcends structural complexity. A first possible reason is that dynamical diversity is strongly amplified by connectome symmetries and the resulting possibility of a multiplicity of ways of breaking these symmetries [8].…”

“…Finally, we adopted here a very simple regional dynamics, with a bistability between just two fixed points, but we expect that using neural masses able to express richer regimes -oscillatory, bursting, chaotic, etc. [15,43,44]-could eventually reduce the sway of connectivity on collective emergent dynamics.…”

“…In particular, based on theoretical neuroscience insight [8,9], one expects that a richly structured "chronnectome"i.e., repertoire of functional connectivity states observed at different times [10]-arises when the noise-driven dynamics of brain networks can sample an equally rich "dynome" [11], i.e. a repertoire of multi-stable dynamical states [12,13] or characteristic transient fluctuation modes [14,15].…”

Introduction to Focus Issue: Nonlinear science of living systems: From cellular mechanisms to functions

“…Large-scale brain phenomena, such as MRI and EEG, are controlled at a lower level by the interaction between individual neurons. Orio et al (2018) investigate synchronization dynamics in large neuronal networks where each neuron is capable of a variety of spiking patterns, including chaos and bursting, and is coupled to its neighbors via gap junctions. They demonstrate that a deterministic network of weakly coupled neurons shows multistable synchrony patterns.…”

“…These modeling approaches have been extended to examine the impact of nonlinear dynamics and noise in higher functions such as psychiatric disorders and in autonomic processes such as stress and sleep (e.g., Braun et al, 2008). The reader will find the HB model used in this Focus Issue for elucidating multi-stable behavior of neural networks (Orio et al, 2018), evaluating the network effects of neuronal diversity (Tchaptchet, 2018), examining synchronization states during sleep and wakefulness (Holmgren Hopkins et al, 2018), and demonstrating synchronous neuronal transitions (Follmann et al, 2018).…”