Chimera resonance in networks of chaotic maps (2307.00006v2)

Abstract: We explore numerically the impact of additive Gaussian noise on the spatio-temporal dynamics of ring networks of nonlocally coupled chaotic maps. The local dynamics of network nodes is described by the logistic map, the Ricker map, and the Henon map. 2D distributions of the probability of observing chimera states are constructed in terms of the coupling strength and the noise intensity and for several choices of the local dynamics parameters. It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance.

• The paper reveals that additive noise can constructively induce chimera states in networks of chaotic maps where deterministic dynamics alone might not, acting similarly to stochastic resonance.
• Researchers used 2D distribution diagrams to show the probability of observing chimera states across varying coupling strength and noise intensity, identifying optimal noise levels for emergence.
• The study highlights noise's nuanced role, showing it can lead to bimodal distributions of chimera probability and also influence coherent windows and solitary states in network dynamics.

Chimera Resonance in Networks of Chaotic Maps: A Study on the Role of Noise

The paper investigates the intriguing phenomenon of chimera resonance in networks of nonlocally coupled chaotic maps subject to additive Gaussian noise. Through a series of computational analyses, the authors, Rybalova et al., explore the constructive impact of noise on chimera states within these networks, challenging the traditional notion of noise as a purely disruptive force.

The research centers on three distinct chaotic maps: the logistic map, the modified Ricker map, and the Henon map. These maps serve as the local dynamics governing individual network nodes. The paper explores the transition between synchronous and asynchronous states in networks, induced not merely by the intrinsic dynamics of the maps but also by external noise, highlighting the non-trivial role of additive Gaussian noise in such transitions.

Key Findings

1. Noise-Induced Chimera States: The critical finding is that noise can facilitate the emergence of chimera states in networks where deterministic dynamics alone may not naturally give rise to such states. This effect is reminiscent of stochastic and coherence resonance phenomena, where a specific level of noise optimizes the probability of observing order (in this case, chimera states).
2. Probability Distributions: The authors develop 2D distribution diagrams showcasing the probability of chimera state observation in the parameter space defined by coupling strength (σ) and noise intensity (D). These diagrams reveal regions where chimera states are most likely to be observed, showing convergence at an optimal noise intensity that maximizes the span of σ over which chimeras are prevalent.
3. Bimodal Distributions: For certain parameter regimes, notably when the local dynamics of the individual maps are near chaotic, the distributions can be bimodal, indicating multiple regimes where chimeras emerge and disappear as noise intensity varies.
4. Coherent Windows and Solitary States: In addition to chimera states, the paper identifies coherent windows and solitary states as part of the network's response to noise. These are transitional regimes where noise either enhances or suppresses synchronization, illustrating the nuanced role of noise in network dynamics.

The findings underscore the importance of noise as a constructive element in complex network dynamics, capable of engendering nonlinear structures that are otherwise absent in deterministic settings. This challenges the oft-held view of noise as a mere perturbative element and opens pathways for its utilization in controlling and harnessing the dynamics of chaotic networks.

Implications and Future Research

The implications of this paper are twofold: theoretically, it advances our understanding of noise as an essential component in nonlinear dynamics; practically, it suggests potential applications in systems where controlled synchronization is desirable. The results may have ramifications in diverse fields such as neuroscience, where neural chimera states could play a critical role in processes like cognitive functioning and information processing, or in engineering, where synchronization of chaotic circuits might be beneficial.

Looking forward, future research could extend these findings by exploring other types of coupling schemes, examining the effects of noise with different statistical properties or correlations, and applying similar methodologies to other classes of dynamical systems. Additionally, experimental validation in physical systems could provide further support for the theoretical predictions presented in this investigation.

In conclusion, this paper serves as a comprehensive exploration into the constructive role of noise in network dynamics, providing a nuanced perspective on noise-induced order in chaotic systems. Through rigorous numerical exploration of chimera states across different chaotic maps, it contributes valuable insights into the emergent behavior of complex systems and the ever-surprising roles that noise can play within them.