相关论文: Criticality or Supersymmetry Breaking ?

Experimental research has shown that the brain's fast electrochemical dynamics, or neurodynamics (ND), is strongly stochastic, chaotic, and instanton (neuroavalanche)-dominated. It is also partly scale-invariant which has been loosely…

Natural dynamics is often dominated by sudden nonlinear processes such as neuroavalanches, gamma-ray bursts, solar flares \emph{etc}. that exhibit scale-free statistics much in the spirit of the logarithmic Ritcher scale for earthquake…

The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found…

Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis which suggests that neural systems reach such a state by self-organizing towards the critical point…

Understanding of short-term synaptic depression (STSD) and other forms of synaptic plasticity is a topical problem in neuroscience. Here we study the role of STSD in the formation of complex patterns of brain rhythms. We use a cortical…

Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A…

Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order's omnipresence has long been recognized by the scientific…

There is a whole range of emergent phenomena in non-equilibrium behaviors can be well described by a set of stochastic differential equations. Inspired by an insight gained during our study of robustness and stability in phage lambda…

A close relation has recently emerged between two of the most fundamental concepts in physics and mathematics: chaos and supersymmetry. In striking contrast to the semantics of the word 'chaos,' the true physical essence of this phenomenon…

Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural…

It was recently established that the formalism of the generalized transfer operator (GTO) of dynamical systems (DS) theory, applied to stochastic differential equations (SDEs) of arbitrary form, belongs to the family of cohomological…

Abrupt shifts in ecosystems, brains, markets, and climate are often diagnosed as signs of approaching a tipping point, i.e. a critical bifurcation where stability is lost. Here we reveal a broader and more deceptive mechanism:…

The observation of apparent power-laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a…

What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…

Chaos and Noise are ubiquitous in the Brain. Inspired by the chaotic firing of neurons and the constructive role of noise in neuronal models, we for the first time connect chaos, noise and learning. In this paper, we demonstrate Stochastic…

The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled…

Dynamics of a chaotic spiking neuron model are being studied mathematically and experimentally. The Nonlinear Dynamic State neuron (NDS) is analysed to further understand the model and improve it. Chaos has many interesting properties such…

Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For…

Self-organized criticality has been proposed to be a universal mechanism for the emergence of scale-free dynamics in many complex systems, and possibly in the brain. While such scale-free patterns were identified experimentally in many…

Further analysis and experimentation is carried out in this paper for a chaotic dynamic model, viz. the Nonlinear Dynamic State neuron (NDS). The analysis and experimentations are performed to further understand the underlying dynamics of…