Related papers: A noise-driven attractor switching device
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
There are certain classes of resistors, capacitors and inductors that, when subject to a periodic input of appropriate frequency, develop hysteresis loops in their characteristic response. Here, we show that the hysteresis of such memory…
Noise appears in the brain due to various sources, such as ionic channel fluctuations and synaptic events. They affect the activities of the brain and influence neuron action potentials. Stochastic differential equations have been used to…
Can noise be beneficial to machine-learning prediction of chaotic systems? Utilizing reservoir computers as a paradigm, we find that injecting noise to the training data can induce a stochastic resonance with significant benefits to both…
Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous…
Adhesive forces are capable of deforming a soft elastic object when it comes in contact with a flat rigid substrate. The contact is in stable equilibrium if the total energy of the system arising from the elastic and surface forces exhibits…
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…
Based on the heuristics that maintaining presumptions can be beneficial in uncertain environments, we propose a set of basic axioms for learning systems to incorporate the concept of prejudice. The simplest, memoryless model of a…
The "edge of chaos" phase transition in artificial neural networks is of renewed interest in light of recent evidence for criticality in brain dynamics. Statistical mechanics traditionally studied this transition with connectivity $k$ as…
A simple threshold model of neuron firing (with the neuron membrane electrochemical potential governed by the chaotic Rossler attractor) has been analyzed by mapping the generated irregular spiking time-series into telegraph signals. In…
Collective rhythmic dynamics from neurons is vital for cognitive functions such as memory formation but how neurons self-organize to produce such activity is not well understood. Attractor-based models have been successfully implemented as…
We studied, both analytically and numerically, complex excitable networks, in which connections are time dependent and some of the nodes remain silent at each time step. More specifically, (a) there is a heterogenous distribution of…
Noise is widely understood to be something that interferes with a signal or process. Thus, it is generally thought to be destructive, obscuring signals and interfering with function. However, early in the 20th century, mechanical engineers…
In this thesis we aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of…
Motivated by a stochastic differential equation describing the dynamics of interfaces, we study the bifurcation behavior of a more general class of such equations. These equations are characterized by a 2-dimensional phase space (describing…
We develop a framework for collective frequency selection and attractor formation by means of delay plasticity. Specifically, we consider adaptive axonal delays (AADs), motivated by activity-dependent myelination in the brain which…
We study an Ising model in a network with disorder induced by the presence of both attractive and repulsive links. This system is subjected to a subthreshold signal, and the goal is to see how the response is enhanced for a given fraction…
Spiking neural networks drawing inspiration from biological constraints of the brain promise an energy-efficient paradigm for artificial intelligence. However, challenges exist in identifying guiding principles to train these networks in a…
We consider the influence of stochastic perturbations on stability of a unique positive equilibrium of a difference equation subject to prediction-based control. These perturbations may be multiplicative $$x_{n+1}=f(x_n)-\left( \alpha +…
Complex physical systems are unavoidably subjected to external environments not accounted for in the set of differential equations that models them. The resulting perturbations are standardly represented by noise terms. We derive conditions…