Research Projects

Symmetry breaking is a fundamental phenomenon observed in physics, chemistry, and biology. Since coupled excitable oscillators represent many natural systems and processes, studies on the noise-induced symmetry-breaking state in coupled excitable systems have been a vibrant area of research over the last decades. Excitability is inherently present in nature . Noise and random fluctuations are present in both natural and man-made systems. In nonlinear systems, noise can result in some ordered dynamical behaviors; examples of these ordered behaviors are coherence resonance [10], and self-induced stochastic resonance(SISR). These noise-induced complex network analyses have been the focus of recent research for the last decade. Using a single isolated neural(FitzHugh-Nagumo) system, DeVille et al analytically illustrate the distinction between coherence resonance (CR) and self-induced stochastic resonance (SISR). Noise may be used to investigate the neuronal dynamical behaviors, which are naturally excitable. The action potential of the neural system may be understood with the help of noise. Noise-activated neurons help humans interpret epileptic seizures. The noise-induced neural system has been less explored in recent years. Semenova et al. first discovered a novel chimera state known as coherence resonance chimera, which is the combination of coherence resonance and classical chimera. The partial synchronization pattern changes depending on the noise intensity for a particular excitable parameter. Motivated by this idea, we established that the coherence resonance chimera indeed general. In addition, we introduced a new chimera pattern known as hybrid coherence resonance chimera, a combination of coherence resonance chimera and classical chimera [13]. Depending on the noise, multiplex neural networks can regulate the CR mechanism via the SISR mechanism in a network of type-II (FHN) neurons. We also discussed the interaction between noise levels in the FHN neural network’s self-induced stochastic resonance activated domain. SISR chimera does not depend on the excitable parameter, but strongly depends on time-scale separation and noise intensity. Another kind of symmetry breaking arises for several numbers of ensembles that interact through nonpairwise interactions; this plays an important role in brain networks and many social networks, known as higher-order interactions. These interactions take place between two or more ensembles at a particular time. As noise-induced collective dynamics is less explored, from the literature review, we observed that noise manifests the most profound effects in understanding the spontaneous symmetry-breaking state in coupled excitable systems. To understand more interesting effects of noise-induced excitable networks, we proposed different types of coupling kernels, such as non-pairwise interaction, which is a less explored coupling kernel in excitable systems.

Noise, Chimera, Aging transition, Higher order interaction,Coherence resonance, Stochastic resonance