相关论文: On transition to bursting via deterministic chaos

Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…

The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…

Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…

Diluted neural networks with continuous neurons and nonmonotonic transfer function are studied, with both fixed and dynamic synapses. A noisy stimulus with periodic variance results in a mechanism for controlling chaos in neural systems…

A bump attractor network is a model that implements a competitive neuronal process emerging from a spike pattern related to an input source. Since the bump network could behave in many ways, this paper explores some critical limits of the…

In this paper we continue to develop our approach to the chaoticity properties of the quantum Hamiltonian systems. Our earlier suggested chaoticity criterion characterizes the initial symmetry breaking and the destruction of the…

In a series of works of ours we have shown that we can represent the critical and tricritical points of the Statistical Physics of critical phenomena as a Dynamical phenomenon expressed by time series produced by the type I intermittency…

An experimental approach is taken to study the dynamics of the dripping water faucet, a simple deterministic system. The time interval between successive drops may be affected by the many drops preceding it. The time interval is predicted…

Numerous systems ranging from deformation of materials to earthquakes exhibit bursty dynamics, which consist of a sequence of events with a broad event size distribution. Very often these events are observed to be temporally correlated or…

This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…

As a promising computational paradigm, occurrence of critical states in artificial and biological neural networks has attracted wide-spread attention. An often-made explicit or implicit assumption is that one single critical state is…

The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…

We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or…

Fluids cooled to the liquid-vapor critical point develop system-spanning fluctuations in density that transform their visual appearance. Despite the rich phenomenology of this critical point, there is not currently an explanation of the…

We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…

The transition from a chaotic to a periodic oscillatory state can be smooth or abrupt in real-world turbulent systems. Although there have been several mathematical studies, the occurrence of abrupt transitions in real-world systems such as…

Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates…

In this paper we address the question of statistical model selection for a class of stochastic models of biological neural nets. Models in this class are systems of interacting chains with memory of variable length. Each chain describes the…

Time-varying connections are crucial in understanding the structures and dynamics of complex networks. In this paper, we propose a continuous-time switching topology model for temporal networks that is driven by bursty behavior and study…

A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…