Publications

Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators' mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups' position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag.© 2023 Author(s). Published under an exclusive license by AIP Publishing.

JTD Keywords: chaos, Generalized synchronization

Abstract Critical dynamics, characterized by scale-free neuronal avalanches, is thought to underlie optimal function in the sensory cortices by maximizing information transmission, capacity, and dynamic range. In contrast, deviations from criticality have not yet been considered to support any cognitive processes. Nonetheless, neocortical areas related to working memory and decision-making seem to rely on long-lasting periods of ignition-like persistent firing. Such firing patterns are reminiscent of supercritical states where runaway excitation dominates the circuit dynamics. In addition, a macroscopic gradient of the relative density of Somatostatin (SST+) and Parvalbumin (PV+) inhibitory interneurons throughout the cortical hierarchy has been suggested to determine the functional specialization of low- versus high-order cortex. These observations thus raise the question of whether persistent activity in high-order areas results from the intrinsic features of the neocortical circuitry. We used an attractor model of the canonical cortical circuit performing a perceptual decision-making task to address this question. Our model reproduces the known saddle-node bifurcation where persistent activity emerges, merely by increasing the SST+/PV+ ratio while keeping the input and recurrent excitation constant. The regime beyond such a phase transition renders the circuit increasingly sensitive to random fluctuations of the inputs -i.e., chaotic-, defining an optimal SST+/PV+ ratio around the edge-of-chaos. Further, we show that both the optimal SST+/PV+ ratio and the region of the phase transition decrease monotonically with increasing input noise. This suggests that cortical circuits regulate their intrinsic dynamics via inhibitory interneurons to attain optimal sensitivity in the face of varying uncertainty. Hence, on the one hand, we link the emergence of supercritical dynamics at the edge-of-chaos to the gradient of the SST+/PV+ ratio along the cortical hierarchy, and, on the other hand, explain the behavioral effects of the differential regulation of SST+ and PV+ interneurons by neuromodulators like acetylcholine in the presence of input uncertainty.

JTD Keywords: attractor model, cortex, cortical networks, edge-of-chaos, model, nmda receptors, Attractor model, Cortical hierarchies, Decision making, Dynamics, Edge of chaos, Edge-of-chaos, High-order, Higher-order, Inhibitory interneurons, Neurons, Optimal decision making, Persistent activities, Persistent activity, Supercritical, Supercriticality

Perceptual decision-making in the brain is commonly modeled as a competition among tuned cortical populations receiving stimulation according to their perceptual evidence. However, the contribution of evidence on the decision-making process changes through time. In this regard, the mechanisms controlling the sensitivity to perceptual evidence remain unknown. Here we explore this issue by using a biologically constrained model of the neocortex performing a dual-choice perceptual discrimination task. We combine mutual and global GABAergic inhibition, which are differentially regulated by acetylcholine (ACh), a neuromodulator linked to enhanced stimulus discriminability. We find that, while mutual inhibition determines the phase-space separation between two stable attractors representing each stimulus, global inhibition controls the formation of a chaotic attractor in-between the two, effectively protecting the weakest stimulus. Hence, under low ACh levels, where global inhibition dominates, the decision-making process is chaotic and less determined by the difference between perceptual evidences. On the contrary, under high ACh levels, where mutual inhibition dominates, the network becomes very sensitive to small differences between stimuli. Our results are in line with the putative role of ACh in enhanced stimulus discriminability and suggest that ACh levels control the sensitivity to sensory inputs by regulating the amount of chaos.

JTD Keywords: Acetylcholine, Cortical model, Decision-making, Chaos

We study two-layer networks of identical phase oscillators. Each individual layer is a ring network for which a non-local intra-layer coupling leads to the formation of a chimera state. The number of oscillators and their natural frequencies is in general different across the layers. We couple the phases of individual oscillators in one layer to the phase of the mean field of the other layer. This coupling from the mean field to individual oscillators is done in both directions. For a sufficient strength of this interlayer coupling, the phases of the mean fields lock across the two layers. In contrast, both layers continue to exhibit chimera states with no locking between the phases of individual oscillators across layers, and the two mean field amplitudes remain uncorrelated. Hence, the networks’ mean fields show phase synchronization which is analogous to the one between low-dimensional chaotic oscillators. The required coupling strength to achieve this mean field phase synchronization increases with the mismatches in the network sizes and the oscillators’ natural frequencies.

JTD Keywords: Chaos, Complex networks, Oscillators, Synchronisation