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In this paper, the stabilization and high efficiency of an unstable Second Harmonic Generation (SHG) of a Nd : YVO4 laser with a KTP intracavity is carried out by using a passive Q-switching crystal and a parametric modulation method (harmonic modulation) is shown. The harmonic modulation was defined as um(t) = Amsin(2π fmt), with modulation amplitude as Am(Vpp), and modulation frequency as fm(Hz), applied to the pumping of the Nd : YVO4 -KTP laser to control the amplitude and frequency of the emission, thus stabilizing the dynamic states of this laser. The promising application of this green light source is materialized when such light is necessary for high-density optics, such as in the treatment materials industry or in some aesthetic applications.

During the past years, the study of optical injection has been intensely carried in theoretical and experimental realizations, showing interesting emergent behaviors, and synchronized states between other results. This work proposes an experimental scheme of an array of three driven erbium-doped fiber lasers (EDFLs), which dynamics exhibit the coexistence of multiple attractors. The laser array is controlled by a driver EDFL by injecting its optical intensity into the three coupled driven EDFLs array. The experimental realization was with the aim to induce an attractor tracking in the driving lasers, then to get coexisting states with increasing output power, and to study other emergent behavior given by the differences between doped fibers. To find the multistability regions, some bifurcation diagrams of the laser peak intensities are constructed. The obtained results are identified by comparing them with the modulation frequency. In some cases, the obtained results show that the intensity of the optical output signal of the driven systems is increased with respect to the initial individual response. In the case of synchronized states, it’s possible to get an increased signal from the whole system. The obtained results could have important applications in repeaters of communications systems.

In this paper, the stabilization and high efficiency of an unstable Second Harmonic Generation (SHG) of an Nd:YVO4 laser with a KTP intracavity is demonstrated. By using a passive Q-switching crystal (Cr4+:YAG) and a parametric modulation method (harmonic modulation), the stabilization of the laser is reached. An harmonic modulation was applied to the pumping of the Nd:YVO4-KTP laser to control the amplitude and frequency of the laser emission. The results were characterized by using power spectra analysis, optical spectrum, bifurcation diagrams, and temporal series of the laser intensity. The promising application of this green light source is materialized when such light is necessary for high-density optics, such as in the treatment materials industry or in some aesthetic applications.

Extreme multistability is the coexistence of a large number of attractors which can be reached by varying initial conditions. In this paper we show how this fascinating phenomenon can be used for secure communication. The main advantage of the communication system based on extreme multistability over a conventional chaos-based communication system is its exceptionally high security. The proposed system consists of two identical six-order oscillators; one in the transmitter and another one in the receiver, each exhibiting the coexistence of a large number of chaotic attractors. The oscillators are synchronized using a private channel through one of the system variables, while the information is transmitted via a public channel through another variable. The information is encrypted by varying the initial condition of one of the state variables in the transmitter using a chaotic map, adhering message packages in a staggered form to the coexisting attractors within the same time series of another state variable, which leads to switching among the coexisting chaotic attractors. To ensure communication security, the duration of the packages is shorter than synchronization time, so that synchronization attacks are ineffective.

In this work, we investigate the Lagrangians and potentials for two coupled damped Duffing oscillators both directionally and bi-directionally. We show that, although it is not always possible to define a potential in dissipative systems, the potential of our model can be defined if the damping coefficient has a logarithmic derivative form. It is possible to apply these results to the analysis of the dynamics of complex networks based on three-node motif configurations. As an example, we study numerically the dynamics for one of the thirteen different possible configurations. Here, the phenomenon of synchronization is observed in terms of the coupling parameter.

We study the emergence of synchronization in the network motif of three bistable Duffing oscillators coupled in all possible configurations. The equation of motion is derived for every configuration. For each motif, we vary initial conditions of every oscillator and calculate the bifurcation diagram as a function of the coupling strength. We find transitions of the whole system to a monostable regime with either a fixed point or a limit cycle depending on the motif’s configuration, as the coupling strength is increased. The most complex dynamics is observed the nidirectional chain, where a transition to quasiperiodicity occurs.

We study noise-induced intermittency in a synergetic model of two coupled oscillators with asymmetric nonlinear coupling. This model was previously used to simulate visual perception of ambiguous images. We show that additive noise induces preference for one of the coexisting unstable steady states. When the noise intensity exceeds a certain threshold value, the oscillations of one of the coupled subsystems are interrupted during some time intervals, resulting in intermittent oscillation death, while another subsystem exhibits noisy oscillations in the vicinity of an unstable fixed point.

In this work, numerical results of a nonlinear switching system that presents bistable attractors subjected to stochastic modulation are shown. The system exhibits a dynamical modification of the bistable attractor, giving rise to an intermit behavior, which depends of modulation strength. The resulting attractor converge to an intermittent double-scroll, for low amplitude modulation, and a 9-scroll attractor for a higher applied noise amplitude. A Detrended Fluctuation Analysis (DFA) applied to the x state variable, shows a perturbations robustness region, since the increase of noise does not present changes. Due to the applied noise, the final obtained system has higher randomness, compared with the original one. The understanding of the dynamical behavior of multiscrolls systems is highly important for advancing technology in communications, as well in memory systems applications.

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.

In this paper, we include simultaneously additive and multiplicative noise to the Pais–Uhlenbeck oscillator (PUO). We construct an integral of motion of the PUO with a time-dependent coefficient. Viewing the PUO as two coupled harmonic oscillators, we add noise to the corresponding frequencies. The systems are solved with the fourth-order stochastic Runge–Kutta method. Some graphics of the solutions and integrals of motion are presented, and the average deviations are calculated in order to quantify the noise influence.

We study dynamics of a ring of three unidirectionally coupled double-well Duffing oscillators for three different values of the damping coefficient: fixed, proportional to time, and inversely proportional to time. The system dynamics in all cases are analyzed using time series, Fourier and Hilbert transforms, Poincare sections, bifurcation diagrams, and Lyapunov exponents for various coupling strengths and damping coefficients. In the first case, we observe a well-known route from a stable steady state to hyperchaos through Hopf bifurcation and a series of torus bifurcations, as the coupling strength is increased. In the second case, the system is highly dissipative and converges into one of the stable equilibria. Finally, in the third case, transient toroidal hyperchaos takes place.

We provide compelling numerical evidence of deterministic coherence and anti-coherence resonance in small networks of unidirectional coupled chaotic Rossler oscillators in star and star-ring configurations in the presence of a small mismatch between natural frequencies of the oscillators. The resonance phenomena are found in both the normalized standard deviations of the peak amplitude and inter-peak time interval with respect to the coupling strength and frequency mismatch. The deterministic coherence/anti-coherence resonance resembles self-stabilization/destabilization of the network when the coupling makes collective dynamics more regular/irregular.

We propose the use of error-feedback control for converting a multistable system into a monostable one. The method is tested with a multistable erbium-doped fiber laser which exhibits the coexistence of four periodic orbits. A desired orbit is selected by an external harmonic modulation which frequency is equal to the frequency of one of the coexisting attractors. Additionally, the error signal, proportional to the difference between the external modulation and the laser output intensity, is applied to the pump current of the diode pumped laser. For certain combinations of the amplitude of the external modulation and the error signal, the laser displays monostability with a single periodic orbit at frequency determined by the external modulation. The efficiency of the control is demonstrated by both numerical simulations and experimentally.

We demonstrate that unidirectional electrical coupling between two periodically spiking Hindmarsh-Rose neurons induces bistability in the system. We find that for certain values of intermediate coupling, the slave neuron exhibits coexistence of two attractors. One of them is the periodic orbit similar to the original attractor without coupling, and the other one is a chaotic attractor or a periodic orbit with higher periodicity, depending on the coupling strength. For strong coupling, the slave neuron is monostable at a periodic orbit similar to the attractor of the master neuron. When the master and slave neurons are in a similar attractor they are completely synchronized, whereas being in different states they are in generalized synchronization. We also present the experimental evidence of this behavior with electronic circuits based on the Hindmarsh-Rose model.

We study synchronization of two chaotic oscillators coupled with time delay in a master-slave configuration and with delayed positive feedback in the slave oscillator which acts as memory. The dynamics of the slave oscillator is analyzed with bifurcation diagrams of the peak value of the system variable with respect to the coupling and feedback strengths and two delay times. For small coupling, when the oscillators’ phases synchronize, memory can induce bistability and stabilize periodic orbits, whereas for stronger coupling it is not possible. The delayed feedback signal impairs synchronization, simultaneously enhancing coherence of the slave oscillator.

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.

We propose an experimental arrangement to increase pulse energy in the array of erbium-doped fiber lasers (EDFLs). The experimental setup consists of three coupled periodically modulated multistable EDFLs; one master laser and two slave lasers. The master laser is tuned to the coexisting attractor with the largest peak amplitude and synchronizes the slave lasers to maintain them in the same attractor as the master laser. Summing the outputs of the slave lasers we obtain laser pulsations with a double peak intensity. The number of slave lasers can be augmented to further increase the sum peak power.

In this paper, a physical interpretation of the fractional-order-derivatives effects in a jerk system, based on Unstable Dissipative Systems (UDS), and a Saturated Non-Linear Function (SNLF), is presented. The system is electronically implemented in Multisim development platform for a 9-scrolls attractor generation. The behavior is analyzed trough the Detrended Fluctuation Analysis (DFA), Probability Density Function (PDF), bifurcation diagrams, and the implementation of a geometrical analysis of the phase space. The changes that the system undergoes when a fractional-order are analyzed. The results show that when the fractional integration-orders are considered, the areas of the generated attractor are modified with respect to the integer-order dynamic. The long-range correlations in the system are also modified because of the fractional-orders. Besides, a particular phenomenon in the equilibrium points preference occurs, which is induced when the fractional integration-order is applied in only one of the state variables.

This paper presents a novel electronic implementation based on a simple methodology to control the number of scrolls generated, by means of operational amplifiers and a single control parameter. Through the use of a Saturated Non Linear Function (SNLF) for the generation of a 9-scroll attractor, the number of scrolls is modified through a single parameter. In addition, the implemented system is also capable of generating a family of bistable behaviors. The phenomenon for the scroll generation, induced by a control parameter, is explained through the system equilibrium points. This methodology can be extended to system’s with higher number of scrolls, or systems with larger basins of attraction. The results shown have high potential application in secure communication systems, mobile surveillance devices, pseudo-random number generators and complex networks, among others.

The increasing usage of chaotic systems in the development of security systems, from mobile surveillance devices to the implementation of secure communication systems, leads to devising analog electronic implementations of research. This article presents the electronic implementation dataset from a multi-scroll chaotic system capable of generates until 9-scrolls throughout a monoparametric control based on a Saturated Non-Lineal Function (SNLF). The implemented system controls the number of generated scrolls being capable of producing attractors of single scroll and attractors with 3, 5, 7, and 9-scrolls. Moreover, the implemented system produces a family of bistable behaviors. The authors report the phenomenon in [1] , where a complete analysis in the system has been carried out.

In this work, we implement multiplicative noise to the Duffing oscillator with variable coefficients. The stochastic differential equations are solved using the fourth-order Runge–Kutta method with the Box-Müller algorithm and the corresponding integral of motion is obtained. Some numerical experiments are performed and the results show that the integral of motion is highly unaffected by the multiplicative noise.

The role of asymmetry in electrical synaptic connection between two neuronal oscillators is studied in the Hindmarsh-Rose model. We demonstrate that the asymmetry induces multistability in spiking dynamics of the coupled neuronal oscillators. The coexistence of at least three attractors, one chaotic and two periodic orbits, for certain coupling strengths is demonstrated with time series, phase portraits, bifurcation diagrams, basins of attraction of the coexisting states, Lyapunov exponents, and standard deviations of peak amplitudes and interspike intervals. The experimental results with analog electronic circuits are in good agreement with the results of numerical simulations.

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 R¨ossler oscillators and the chaotic logistic map. The latter is used for fast variation of the most sensitive system parameter when the R¨ossler oscillators synchronize. The algorithm is robust to noise in the communication channel.

We experimentally studied dynamics of a dual-cavity Nd:YAG laser with second harmonic generation in one of the cavities and loss modulation in another cavity. Dependent on the frequency of harmonic modulation of the infrared light, we observed the coexistence of different correlated and uncorrelated regimes of the infrared and green outputs from two laser cavities. We present the experimental evidence of oscillation death coexistent with oscillatory states for certain modulation frequencies.

We implement a dynamic logic gate which consists of three elements: a chaotic fiber laser, a threshold controller and the output of the logic gate. The output signal of the fiber laser is sent to the logic gate input as to the threshold controller; threshold controller output signal is sent at the entrance of the logic gate and also feedback to the fiber laser which changes their dynamic behavior. The output of the logic gate consists of a difference amplifier; this compares the signals sent by the threshold controller and the fiber laser, resulting logic output that depend on an accessible parameter in threshold controller. We present the numerical results and experimental of the implementation of a dynamic logic gate using fiber laser, which demonstrates the ability to change the type of logic gate by modifying a parameter of threshold control.

Synchronization of chaotic oscillators has an important application in cryptography. When two identical oscillators are coupled, they can be completely synchronized and the chaotic output of the transmitter oscillator can be used to mask a message. Although the oscillator parameters are usually used as secret keys, the sensitivity of such cryptosystems to parameter changes has never been systematically analyzed. To cryptanalyze a communication system based on synchro- nization of chaotic oscillators, we use a synchronization attack that allows estimating all unknown parameters by minimizing the synchronization error. Using this attack we cryptanalyze popular communication systems based on the Rossler and Chua chaotic electronic circuits. We suggest to include this attack as a standard security test for crypt-analysis of chaotic communication systems.

In the last decade, complex networks have widely been applied to the study of many natural and man-made systems, and to the extraction of meaningful information from the interaction structures created by genes and proteins. Nevertheless, less attention has been devoted to metabonomics, due to the lack of a natural network representation of spectral data. Here we define a technique for reconstructing networks from spectral data sets, where nodes represent spectral bins, and pairs of them are connected when their intensities follow a pattern associated with a disease. The structural analysis of the resulting network can then be used to feed standard data-mining algorithms, for instance for the classification of new (unlabeled) subjects. Furthermore, we show how the structure of the network is resilient to the presence of external additive noise, and how it can be used to extract relevant knowledge about the development of the disease.

We propose and implement experimentally an opto-electronic chaotic communication system based on chaos synchronization, which uses two channels: the electronic channel for synchronization and the optical channel for information transmission. Both the transmitter and the receiver contain identical chaotic Rossler-like electronic circuits and identical continuous wave semiconductor lasers. The circuit in the receiver is synchronized with the circuit in the transmitter by one of the variables via the electronic channel, while another variable serves to drive the laser pump current chaotically. Due to the functional dependence of the circuit variables, the signals transmitted through the electronic and optical channels are also functionally dependent. A message is encrypted into the laser output in the transmitter and sent to the receiver via the optical channel, where the received waveform is compared with the laser output in the receiver. Since the lasers in the transmitter and in the receiver are completely synchronized, the message is retrieved with a very good precision.

We propose a method for the detection and localization of different types of coexisting oscillatory regimes that alternate with each other leading to multistate intermittency. Our approach is based on consideration of wavelet spectrum energies. The proposed technique is tested in an erbium-doped fiber laser with four coexisting periodic orbits, where external noise induces intermittent switches between the coexisting states. Statistical characteristics of multistate intermittency, such as the mean duration of the phases for every oscillation type, are examined with the help of the developed method. We demonstrate strong advantages of the proposed technique over previously used amplitude methods.