Patrick Louodop

A strategy for adaptive synchronization of an electrical chaotic circuit based on nonlinear control

This paper deals with the adaptive synchronization of an electrical chaotic oscillator through a nonlinear control law. The nonlinear controller is designed to synchronize two identical chaotic systems. Lyapunov stability theory is applied to prove that under some conditions the drive-response system can achieve practical synchronization. The designed controller contains only continuous nonlinear terms existing in the dynamical systems and is easy to implement in practice. As an illustrative example to verify the validity of the proposed method, a hyperbolic tangent-based electrical and chaotic circuit is chosen and its dynamics is briefly investigated to demonstrate its chaotic behavior.

Adaptive time-delay synchronization of chaotic systems with uncertainties using a nonlinear feedback coupling

This paper treats the adaptive synchronization problem of a class of uncertain chaotic systems with uncertainties, delay and unknown inputs in a drive-response framework. A robust adaptive observer-based response system is designed to synchronize a given delayed chaotic system without the knowledge of upper bounds of uncertainties and unknown inputs. Furthermore, the unknown inputs can be approximately recovered directly by the concept of equivalent control signal. To highlight our method, we improve the robustness of ciphering in a secure communication system. Computer simulation is also given for the purpose of illustration and verification.

Finite-time synchronization of Lorenz chaotic systems: theory and circuits

This paper addresses the problem of finite-time master–slave synchronization of Lorenz chaotic systems from a control theoretic point of view. We propose a family of feedback couplings which accomplish the synchronization of Lorenz chaotic systems based on Lyapunov stability theory. These feedback couplings are based on non-periodic functions. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at established time. An advantage is that some of the proposed feedback couplings are simple and easy to implement. Both mathematical investigations and numerical simulations followed by a Pspice experiment are presented to show the feasibility of the proposed method.

Finite-time synchronization of tunnel-diode-based chaotic oscillators.

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel-diode-based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulations followed by pspice experiment are presented to show the feasibility of the proposed method.

Coherent libration to coherent rotational dynamics via chimeralike states and clustering in a Josephson junction array

An array of excitable Josephson junctions under a global mean-field interaction and a common periodic forcing shows the emergence of two important classes of coherent dynamics, librational and rotational motion, in the weaker and stronger coupling limits, respectively, with transitions to chimeralike states and clustered states in the intermediate coupling range. In this numerical study, we use the Kuramoto complex order parameter and introduce two measures, a libration index and a clustering index, to characterize the dynamical regimes and their transitions and locate them in a parameter plane.

A novel high-frequency interpretation of a general purpose Op-Amp-based negative resistance for chaotic vibrations in a simple a priori nonchaotic circuit

A novel model of general purpose operational amplifiers is made to approximate, at best, the equivalent circuit for real model at high-frequency. With this new model, it appears that certain oscillators, usually studied under ideal considerations or using many existing real models of operational amplifiers, have hidden subtle and attractive chaotic dynamics that have previously been unknown. These can now be revealed. With the new considerations, a “two-component” circuit, consisting simply of a capacitor in parallel with a nonmodified (and usually presented as a linear, negative) resistance, tends to exhibit chaotic signals. P-Spice and laboratory experimental results are in good agreement with the theoretical predictions.

Optimal Synchronization of a Memristive Chaotic Circuit

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

Coherent motion of chaotic attractors

We report a simple model of two drive-response-type coupled chaotic oscillators, where the response system copies the nonlinearity of the driver system. It leads to a coherent motion of the trajectories of the coupled systems that establishes a constant separating distance in time between the driver and the response attractors, and their distance depends upon the initial state. The coupled system responds to external obstacles, modeled by short-duration pulses acting either on the driver or the response system, by a coherent shifting of the distance, and it is able to readjust their distance as and when necessary via mutual exchange of feedback information. We confirm these behaviors with examples of a jerk system, the paradigmatic Rössler system, a tunnel diode system and a Josephson junction-based jerk system, analytically, to an extent, and mostly numerically.

Optimisation of the synchronisation of a class of chaotic systems: combination of sliding mode and feedback control

This paper addresses the problem of optimisation of the synchronisation for a class of uncertain chaotic systems from a control theoretic point of view. A robust adaptive feedback which accomplishes the synchronisation of chaotic systems using an optimal tuning scheme based on Riccatti equations is successfully adapted. The underlying idea is to optimise the synchronisation of chaotic systems by accounting the control effort despite the uncertainties. The approach developed considers incomplete state measurements and no detailed model of the systems to guarantee robust stability. This approach includes a high-order sliding mode estimator and leads to a robust adaptive feedback control scheme. A finite horizon can be arbitrarily established by ensuring that the chaos synchronisation is achieved at established time. An advantage is that the studied scheme accounts the energy wasted by the controller and the closed-loop performance on synchronisation. Both mathematic proof and numerical simulations are presented o show the feasibility of the optimisation strategy for establishing the synchronisation of chaotic systems even if there are some modelling mismatches and parametric variations.