[Paper Review] Noise-induced chimera states in a neural network

Anna Zakharova, Nadezhda Semenova+2 more|arXiv (Cornell University)|Nov 10, 2016

Nonlinear Dynamics and Pattern Formation72 references5 citations

TL;DR

This paper demonstrates that noise can induce chimera states in nonlocally coupled neural networks operating in the excitable regime, revealing a novel phenomenon termed 'coherence-resonance chimeras.' These patterns emerge at intermediate noise intensities, exhibit alternating coherent and incoherent domains, and result from the constructive interplay between coherence resonance and chimera dynamics.

ABSTRACT

We show that chimera patterns can be induced by noise in nonlocally coupled neural networks in the excitable regime. In contrast to classical chimeras, occurring in noise-free oscillatory networks, they have features of two phenomena: coherence resonance and chimera states. Therefore, we call them coherence-resonance chimeras. These patterns demonstrate the constructive role of noise and appear for intermediate values of noise intensity, which is a characteristic feature of coherence resonance. In the coherence-resonance chimera state a neural network of identical elements splits into two coexisting domains with different behavior: spatially coherent and spatially incoherent, a typical property of chimera states. Moreover, these noise-induced chimera states are characterized by alternating behavior: coherent and incoherent domains switch periodically their location. We show that this alternating switching can be explained by analyzing the coupling functions.

Motivation & Objective

• To investigate whether chimera states can emerge in excitable neural networks, which have not been observed in noise-free conditions.
• To explore the role of noise in inducing and controlling chimera states in nonlocally coupled systems.
• To identify a new class of chimera states that combine coherence resonance and spatial pattern formation.
• To explain the alternating behavior of coherent and incoherent domains in terms of coupling function dynamics.
• To propose a mechanism for unihemispheric sleep based on noise-driven spatiotemporal pattern switching.

Proposed method

• Modeling a ring of $ N $ nonlocally coupled FitzHugh-Nagumo (FHN) neurons with Gaussian white noise using stochastic differential equations.
• Using a coupling scheme with range $ R $, where each neuron interacts with neighbors within a fixed spatial window via $ b_{uu}, b_{uv}, b_{vu}, b_{vv} $ coupling coefficients.
• Applying noise intensity $ D $ as a control parameter to probe the emergence of coherence-resonance chimeras.
• Analyzing spatiotemporal dynamics through time-series simulations and space-time plots to identify coherent and incoherent domains.
• Defining key observables: normalized incoherent domain size $ ho = rac{ ho}{N} $, active time span $ riangle $, and noise-dependent pattern transitions.
• Employing parameter sweeps over $ a $ (excitation threshold) and $ D $ (noise intensity) to map the existence region of coherence-resonance chimeras.

Experimental results

Research questions

• RQ1 Can chimera states be induced in excitable neural networks by noise, despite their absence in noise-free conditions?
• RQ2 Does the emergence of chimera states in excitable systems exhibit characteristics of coherence resonance, such as optimal noise intensity?
• RQ3 What causes the periodic switching between coherent and incoherent domains in the observed chimera patterns?
• RQ4 How does the size of the incoherent domain depend on noise intensity and excitation threshold $ a $?
• RQ5 Can this noise-induced chimera state provide a plausible mechanism for unihemispheric sleep in animals?

Key findings

• Coherence-resonance chimeras emerge only for intermediate noise intensities $ D riangleq 0.000062 $ to $ 0.000325 $, confirming the hallmark of coherence resonance.
• The normalized size of the incoherent domain $ ho/N $ increases with noise intensity $ D $, while the active time span $ riangle $ remains approximately constant across the interval.
• Chimera states exist only within a narrow range of the excitation threshold $ a $, specifically $ 0.995 riangleq a riangleq 1.004 $, beyond which the system becomes fully synchronized or fully incoherent.
• The coherent and incoherent domains periodically switch positions, a dynamic feature linked to the structure of the coupling functions and noise-induced spatiotemporal dynamics.
• The system transitions between steady state, coherence-resonance chimera, and traveling wave patterns depending on noise intensity and $ a $, demonstrating noise-based control of network states.
• The findings suggest that noise can serve as a control mechanism for neural network patterns, offering a potential explanation for unihemispheric sleep via alternating hemispheric synchronization.