Related papers: Cupolets in a Chaotic Neuron Model
This paper discusses applications of a particular control technique that can be used to very efficiently stabilize a chaotic system onto a large subset of the unstable periodic orbits that are typically embedded in the system. The control…
This paper investigates the origin and onset of chaos in a mathematical model of an individual neuron, arising from the intricate interaction between 3D fast and 2D slow dynamics governing its intrinsic currents. Central to the chaotic…
We investigate the impact of magnetic-field-induced feedback on the dynamics of a Hindmarsh-Rose neuron model exhibiting a blue-sky catastrophe. By introducing a magnetic flux variable that couples nonlinearly to the membrane potential, we…
Heteroclinic cycles are widely used in neuroscience in order to mathematically describe different mechanisms of functioning of the brain and nervous system. Heteroclinic cycles and interactions between them can be a source of different…
Transport of neural signals in the brain is challenging, owing to neural interference and neural noise. There is experimental evidence of multiplexing of sensory information across population of neurons, particularly in the vertebrate…
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic…
In large-scale neural networks, coherent limit cycle oscillations usually coexist with unstable incoherent equilibrium states, which are not observed experimentally. We implement a first-order dynamic controller to stabilize unknown…
In this paper, we address the reduced-order synchronization problem between two chaotic memristive Hindmarsh-Rose (HR) neurons of different orders using two distinct methods. The first method employs the Lyapunov active control technique.…
In this contribution, we have considered the collective behavior of the two as well as the network of heterogeneous coupled Hindmarsh Rose (HR) neurons. The heterogeneous models were made of a memristive 2D (HR) and the traditional 3D HR…
We propose to control the orbits of the two-dimensional Rulkov model affected by bounded noise. For the correct parameter choice the phase space presents two chaotic regions separated by a transient chaotic region in between. One of the…
A theoretical analysis of two- and three-dimensional fractional-order Hindmarsh-Rose neuronal models is presented, focusing on stability properties and occurrence of Hopf bifurcations, with respect to the fractional order of the system…
In this paper, we have introduced and investigated the collective behavior of a network of memristive Hindmarsh-Rose (HR) neurons. The proposed model was built considering the memristive autapse of the traditional 2D HR neuron. Using the…
Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons, lasers, chemical reactions, arrhythmic cardiac tissue, and spontaneously bursting neuronal networks. An underlying…
We analyze the dynamics of a deterministic model of inhibitory neuronal networks proving that the discontinuities of the Poincare map produce a never empty chaotic set, while its continuity pieces produce stable orbits. We classify the…
One of the common characteristics of chaotic maps or flows in high dimensions is "unstable dimensional variability", in which there are periodic points whose unstable manifolds have different dimensions. In this paper, in trying to…
Based on the invariance principle of differential equations a simple, systematic, and rigorous feedback scheme with the variable feedback strength is proposed to stabilize nonlinearly any chaotic systems without any prior analytical…
Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to…
We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear…
A neural network model that exhibits stochastic population bursting is studied by simulation. First return maps of inter-burst intervals exhibit recurrent unstable periodic orbit (UPO)-like trajectories similar to those found in experiments…
Neuronal systems have been modeled by complex networks in different description levels. Recently, it has been verified that networks can simultaneously exhibit one coherent and other incoherent domain, known as chimera states. In this work,…