Sifeu Takougang Kingni

Three-Dimensional Chaotic Autonomous System with a Circular Equilibrium: Analysis, Circuit Implementation and Its Fractional-Order Form

A three-dimensional autonomous chaotic system with a circular equilibrium is investigated in this paper. Some dynamical properties and behaviors of this system are described in terms of equilibria, eigenvalue structures, bifurcation diagrams, Lyapunov exponents, time series and phase portraits. For specific parameters, the system displays periodic and chaotic attractors. The physical existence of the chaotic behavior found in the proposed system is verified by using the Orcad-PSpice software and experimental verification. A good qualitative agreement is shown between the experimental results, PSpice and numerical simulations. Furthermore, the commensurate fractional-order version of the system with a circular equilibrium is numerically studied. It is found that chaos exists in this system with order less than three. By tuning the commensurate fractional order, the system with a circular equilibrium displays chaotic and periodic attractors, respectively. Finally, chaos synchronization of identical fractional-order chaotic systems with a circular equilibrium is achieved by using the unidirectional linear error feedback coupling. It is shown that the fractional-order chaotic system can achieve synchronization for appropriate coupling strength.

The Relationship Between Chaotic Maps and Some Chaotic Systems with Hidden Attractors

In this note, hidden attractors in chaotic maps are investigated. Although there are many new researches on hidden attractors in chaotic flows, no investigation has been done on hidden attractors in maps based on our knowledge. In addition, a new interesting chaotic map with a bifurcation diagram starting from any desired period and then continuing with period doubling is introduced in this paper.

Direct modulation of semiconductor ring lasers: numerical and asymptotic analysis

We investigate numerically the dynamical behavior in a semiconductor ring laser (SRL) subject to a periodic modulation of the injection current. By varying the amplitude and frequency of the modulation at a fixed bias current, different dynamical states including periodic, quasi-periodic, and chaotic states are found. At frequencies comparable to the relaxation oscillation frequency, the intensities of the counterpropagating modes of the SRLs may exhibit in-phase chaotic motion similar to single mode semiconductor lasers. However, antiphase chaotic oscillations in the modal intensities are observed for modulation frequencies significantly lower than the relaxation oscillations frequency. We show that this antiphase chaotic regime does not involve carrier dynamics and is a result of the underlying symmetry of the SRL. We derive a two-dimensional asymptotic model valid on time-scales longer than the relaxation oscillations, which reproduces the observed dynamical behavior. In a further simplification, we can link this reduced set of equations to Duffing-type oscillators.

Constructing and analyzing of a unique three-dimensional chaotic autonomous system exhibiting three families of hidden attractors

A three-dimensional chaotic autonomous system is proposed in this paper. This system has a unique property: it can belong to three different families of chaotic systems with hidden attractors: (a) systems with a line of equilibria, (b) systems with only stable equilibria, and (c) systems with no equilibria. Dynamics of this system are investigated through eigenvalue structures, phase portraits, basin of attraction, bifurcation diagram and Lyapunov exponents. The physical existence of the chaotic behavior found in the proposed system is verified by using OrCAD-PSpice software. A good qualitative agreement is shown between the simulations and the PSpice results.

Generating a Chaotic System with One Stable Equilibrium

Although chaotic systems with hidden attractors have been discovered recently, there are few investigations about relationships among them. This brief work introduces a novel chaotic system with only one stable equilibrium that is constructed by adding a tiny perturbation into a known chaotic flow having hidden attractors with a line equilibrium.

Semiconductor lasers driven by self-sustained chaotic electronic oscillators and applications to optical chaos cryptography.

In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chuas oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate.

A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

No-equilibrium system with chaotic behavior has attracted considerable attention recently because of its hidden attractor. We study a new four-dimensional system without equilibrium in this work. The new no-equilibrium system exhibits hyperchaos and coexisting attractors. Amplitude control feature of the system is also discovered. The commensurate fractional-order version of the proposed system is studied using numerical simulations. By tuning the commensurate fractional-order, the proposed system displays a wide variety of dynamical behaviors ranging from coexistence of quasiperiodic and chaotic attractors and bistable chaotic attractors to point attractor via transient chaos.

Rogue waves in Lugiato-Lefever equation with variable coefficients

In this paper, we theoretically investigate the generation of optical rogue waves from a Lugiato-Lefever equation with variable coefficients by using the nonlinear Schrödinger equation-based constructive method. Exact explicit rogue-wave solutions of the Lugiato-Lefever equation with constant dispersion, detuning and dissipation are derived and presented. The bright rogue wave, intermediate rogue wave and the dark rogue wave are obtained by changing the value of one parameter in the exact explicit solutions corresponding to the external pump power of a continuous-wave laser.

Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system

ABSTRACT This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master–slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

Parameter Identification of a Chaotic Circuit with a Hidden Attractor Using Krill Herd Optimization

Parameter estimation plays an important role in modeling and system identification. However, parameter estimation of chaotic systems has some basic differences with other dynamical systems due to butterfly effect. In this paper, we apply a new cost function for parameter estimation in a very interesting chaotic system, a system with a plane of equilibrium which belongs to a newly introduced category of dynamical systems: systems with hidden attractor. The nonlinear dynamics of this system is described in terms of equilibria and its stability, phase portraits, bifurcation diagram and Lyapunov exponents. In order to minimize the proposed cost function and obtain the correct parameters, we use a new efficient optimization method, Krill Herd algorithm. The results show the success of proposed procedures.