Selective monostability in multi-stable systems

We propose a robust method that allows a periodic or a chaotic multi-stable system to be transformed to a monostable system at an orbit with dominant frequency of any of the coexisting attractors. Our approach implies the selection of a particular attractor by periodic external modulation with frequency close to the dominant frequency in the power spectrum of a desired orbit and simultaneous annihilation of all other coexisting states by positive feedback, both applied to one of the system parameters. The method does not require any preliminary knowledge of the system dynamics and the phase space structure. The efficiency of the method is demonstrated in both a non-autonomous multi-stable laser with coexisting periodic orbits and an autonomous Rössler-like oscillator with coexisting chaotic attractors. The experiments with an erbium-doped fibre laser provide evidence for the robustness of the proposed method in making the system monostable at an orbit with dominant frequency of any preselected attractor

Mathematical modeling of neuronal connexin-36 channels

Neurotransmission through electrical synapses play an important role in the spike synchrony among neurons and oscillation of neuron networks. Connexin36 (Cx36) is the principal gap junction protein of electrical synapses between inhibitory interneurons in vertebrates. Coupling strength between coupled neurons is modulated, among other factor, by the voltage difference between cell interiors, termed transjunctional voltage (Vj), in a complex manner; with the Vj gradient junctional conductance of Cx36 channels first increases instantaneously (+ 20% for + 100 mV) and then it decreases slowly to half for a similar range of Vj. The significance of this regulation by voltage, a stimulus always presents and changing, in the firing properties of coupled neurons is unknown

Experimental and Numerical Study of an Optoelectronics Flexible Logic Gate Using a Chaotic Doped Fiber Laser

In this chapter, we present the experimental and numerical study of an optoelectronics flexible logic gate using a chaotic erbium-doped fiber laser. The implementation consists of three elements: a chaotic erbium-doped fiber laser, a threshold controller, and the logic gate output. The output signal of the fiber laser is sent to the logic gate input as the threshold controller. Then, the threshold controller output signal is sent to the input of the logic gate and fed back to the fiber laser to control its dynamics. The logic gate output consists of a difference amplifier, which compares the signals sent by the threshold controller and the fiber laser, resulting in the logic output, which depends on an accessible parameter of the threshold controller. The dynamic logic gate using the fiber laser exhibits high ability in changing the logic gate type by modifying the threshold control parameter

How to resist synchronization attacks

Conventional synchronization-based chaotic communication is vulnerable to synchronization attacks enable to recuperate system parameters. However, it is possible to make these attacks inefficient. The simple way to resist synchronization attacks is to change a parameter of the master system faster than the time needed for the system to synchronize. To verify this idea we construct a hybrid communication system composed of two chaotic Rössler oscillators and the chaotic logistic map. The latter is used for fast variation of the most sensitive system parameter when the Rössler oscillators synchronize. The algorithm is robust to noise in the communication channel

Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator

In this paper, we propose using paraxial matrix optics to describe a ring-phase conjugated resonator that includes an intracavity chaos-generating element; this allows the system to behave in phase space as a Bogdanov Map. Explicit expressions for the intracavity chaos-generating matrix elements were obtained. Furthermore, computer calculations for several parameter configurations were made; rich dynamic behavior among periodic orbits high periodicity and chaos were observed through bifurcation diagrams. These results confirm the direct dependence between the parameters present in the intracavity chaos-generating element

Bistability in Hindmarsh-Rose oscillators induced by asymmetric electrical coupling

In this paper, we are interested in the question of how bistability can appear in coupled neurons. Concrete motivation for such a general problem is the search for a way to destroy an organism having a stable dynamics by destabilizing its metabolism. To address this issue, we consider the model of a pair of neuron cells coupled via an electrical synapse. We focus on the HindmarshRose model which provides a simple description of the patterned activity observed in molluscan neurons. The results of numerical simulations show that asymmetric electrical coupling between periodically spiking neural oscillators results in bistability in this system. One of the coexisting attractors is a limit cycle similar to the attractor of the uncoupled neuron, while the other one can be either a chaotic or a periodic orbit depending on the coupling strengths. Bistability is only observed for relatively small couplings. When the coupling is sufficiently strong, the neurons are in a monostable periodic regime, similar to the spiking regime observed in the uncoupled neurons

Bistability in Hindmarsh-Rose oscillators induced by asymmetric electrical coupling

In this paper, we are interested in the question of how bistability can appear in coupled neurons. Concrete motivation for such a general problem is the search for a way to destroy an organism having a stable dynamics by destabilizing its metabolism. To address this issue, we consider the model of a pair of neuron cells coupled via an electrical synapse. We focus on the HindmarshRose model which provides a simple description of the patterned activity observed in molluscan neurons. The results of numerical simulations show that asymmetric electrical coupling between periodically spiking neural oscillators results in bistability in this system. One of the coexisting attractors is a limit cycle similar to the attractor of the uncoupled neuron, while the other one can be either a chaotic or a periodic orbit depending on the coupling strengths. Bistability is only observed for relatively small couplings. When the coupling is sufficiently strong, the neurons are in a monostable periodic regime, similar to the spiking regime observed in the uncoupled neurons

Deterministic Brownian-like Motion: Electronic Approach

Brownian motion is a dynamic behavior with random changes over time (stochastic) that occurs in many vital functions related to fluid environments, stock behavior, or even renewable energy generation. In this paper, we present a circuit implementation that reproduces Brownian motion based on a fully deterministic set of differential equations. The dynamics of the electronic circuit are characterized using four well-known metrics of Brownian motion, namely: (i) Detrended Fluctuation Analysis (DFA), (ii) power law in the power spectrum, (iii) normal probability distribution, and (iv) Mean Square Displacement (MSD); where traditional Brownian motion exhibits linear time growth of the MSD, a Gaussian distribution, a −2 power law of the frequency spectrum, and DFA values close to 1.5. The obtained results show that for a certain combination of values in the deterministic model, the dynamics in the electronic circuit are consistent with the expectations for a stochastic Brownian behavior. The presented electronic circuit improves the study of Brownian behavior by eliminating the stochastic component, allowing reproducibility of the results through fully deterministic equations, and enabling the generation of physical signals (analog electronic signals) with Brownian-like properties with potential applications in fields such as medicine, economics, genetics, and communications, to name a few

Deterministic Brownian-like Motion: Electronic Approach

Brownian motion is a dynamic behavior with random changes over time (stochastic) that occurs in many vital functions related to fluid environments, stock behavior, or even renewable energy generation. In this paper, we present a circuit implementation that reproduces Brownian motion based on a fully deterministic set of differential equations. The dynamics of the electronic circuit are characterized using four well-known metrics of Brownian motion, namely: (i) Detrended Fluctuation Analysis (DFA), (ii) power law in the power spectrum, (iii) normal probability distribution, and (iv) Mean Square Displacement (MSD); where traditional Brownian motion exhibits linear time growth of the MSD, a Gaussian distribution, a −2 power law of the frequency spectrum, and DFA values close to 1.5. The obtained results show that for a certain combination of values in the deterministic model, the dynamics in the electronic circuit are consistent with the expectations for a stochastic Brownian behavior. The presented electronic circuit improves the study of Brownian behavior by eliminating the stochastic component, allowing reproducibility of the results through fully deterministic equations, and enabling the generation of physical signals (analog electronic signals) with Brownian-like properties with potential applications in fields such as medicine, economics, genetics, and communications, to name a few

Numerical and Experimental Data of the Implementation of Logic Gates in an Erbium-Doped Fiber Laser (EDFL)

In this article, the methods for obtaining time series from an erbium-doped fiber laser (EDFL) and its numerical simulation are described. In addition, the nature of the obtained files, the meaning of the changing file names, and the ways of accessing these files are described in detail. The response of the laser emission is controlled by the intensity of a digital signal added to the modulation, which allows for various logical operations. The numerical results are in good agreement with experimental observations. The authors provide all of the time series from an experimental implementation where various logic gates are obtained