Oscillations and chaos in neural networks: an exactly solvable model.

نویسندگان

L P Wang

E E Pichler

J Ross

چکیده

We consider a randomly diluted higher-order network with noise, consisting of McCulloch-Pitts neurons that interact by Hebbian-type connections. For this model, exact dynamical equations are derived and solved for both parallel and random sequential updating algorithms. For parallel dynamics, we find a rich spectrum of different behaviors including static retrieving and oscillatory and chaotic phenomena in different parts of the parameter space. The bifurcation parameters include first- and second-order neuronal interaction coefficients and a rescaled noise level, which represents the combined effects of the random synaptic dilution, interference between stored patterns, and additional background noise. We show that a marked difference in terms of the occurrence of oscillations or chaos exists between neural networks with parallel and random sequential dynamics.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Noise-induced phase transitions in neuronal networks

Using an exactly solvable cortical model of a neuronal network, we show that, by increasing the intensity of shot noise (flow of random spikes bombarding neurons), the network undergoes first-and second-order non-equilibrium phase transitions. We study the nature of the transitions, bursts and avalanches of neuronal activity. Saddle-node and supercritical Hopf bifurcations are the mechanisms of...

متن کامل

The maximal family of exactly solvable chaos

A new two-parameter family of ergordic transformations with non-uniform invariant measures on the unit interval I = [0, 1] is found here. The family has a special property that their invariant measures can be explicitly written in terms of algebraic functions of parameters and a dynamical variable. Furthermore, it is also proven here that this family is the most generalized class of exactly sol...

متن کامل

Chaotic Test and Non-Linearity of Abnormal Stock Returns: Selecting an Optimal Chaos Model in Explaining Abnormal Stock Returns around the Release Date of Annual Financial Statements

For many investors, it is important to predict the future trend of abnormal stock returns. Thus, in this research, the abnormal stock returns of the listed companies in Tehran Stock Exchange were tested since 2008- 2017 using three hypotheses. The first and second hypotheses examined the non-linearity and non-randomness of the abnormal stock returns ′ trend around the release date of annual fin...

متن کامل

Neural networks with dynamical synapses: from mixed-mode oscillations and spindles to chaos

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 circuit model of neural networks composed of irregular spiking excitatory and inhibitory neurons having type 1 and 2 excitability and stochastic dynamics. In the...

متن کامل