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We study a van der Pol-like memristor oscillator, obtained by substituting a Chua's diode with an active controlled memristor in a van der Pol oscillator with Chua's diode. The mathematical model for the studied circuit is given by a three-dimensional piecewise linear system of ordinary differential equations, depending on five parameters. We show that this system has a line of equilibria given by the -axis and the phase space is foliated by invariant planes transverse to this line, which implies that the dynamics is essentially two-dimensional. We also show that in each of these invariant planes may occur limit cycles and relaxation oscillations (that is, nonsinusoidal repetitive (periodic) solutions), depending on the parameter values. Hence, the oscillator studied here, constructed with a memristor, is also a relaxation oscillator, as the original van der Pol oscillator, although with a main difference: in the case of the memristor oscillator, an infinity of oscillations are produced, one in each invariant plane, depending on the initial condition considered. We also give conditions for the nonexistence of oscillations, depending on the position of the invariant planes in the phase space. [ABSTRACT FROM AUTHOR]

This paper investigates the global lagged finite-time synchronization of the master-slave Lur'e systems subject to time delay of signal transmission. By designing a variable-substitution and feedback controller, a master-slave finite-time synchronization scheme for the Lur'e systems with time delay is built up. Two delay-independent global lagged finite-time synchronization criteria are proved in the forms of linear matrix inequalities (LMIs), and the corresponding settling time of synchronization is analytically estimated. The obtained LMI criteria are applied to Chua's oscillators, obtaining some easily implemented algebraic criteria under various single-variable-substitution and feedback controller, which are then optimized to improve their conservative property. Finally, several numerical examples are illustrated to verify the effectiveness of the optimized criteria. [ABSTRACT FROM AUTHOR]

In this paper, we develop a parameter matching technique using adaptive synchronization with a chaotic attractor. Two Chua's oscillators, identical in every parameter except for one, are set-up in a master/slave configuration where the slave's mismatched parameter is adaptable. Using Lyapunov functions and incorporating the presence of chaotic signals, adaptive control laws are designed to ensure exact parameter matching. One of the derived adaptive controllers is experimentally validated by using an adaptive inductor-gyrator composed of current feedback op-amps (CFOAs). The experimental results are compared to high-fidelity SPICE simulations, and performance of adaptive controllers are compared over a wide range of parameter values using MATLAB. [ABSTRACT FROM AUTHOR]

This paper presents the universality of the coexistence of complete synchronization with the recently new proposed inverse π-lag synchronization, in the case of mutually coupled systems of Chua's circuit family. The phenomenon of multistability and the nature of this circuit family systems are the key-points which lead to the explanation of this coexistence. For the need of this work, the most representative circuit of this circuits' family, the Chua oscillator, is used. Simulation results confirm this universality in the class of Chua's circuit family. [ABSTRACT FROM AUTHOR]

The modeling and numerical investigation of the dynamical behavior of a semiconductor ring laser (SRL) driven by Chua’s oscillator are reported. By increasing the coupling strength between the SRL and Chua’s oscillator at a fixed bias current, the SRL exhibits an intermittency route to anti-phase chaos. However, for a fixed value of the coupling strength, we report a period-doubling route to out-of-phase and anti-phase chaos when varying one of the parameters of the Chua’s oscillator are reported. We also demonstrate that a SRL driven by the chaotic output of Chua’s oscillator generates a more complex chaos compared to the one found in a SRL subject to a sinusoidally modulated current. This new way of modulation of semiconductor lasers would not only bring a general benefit in the physical equipment and reduce their cost but could have an impact for some relevant engineering applications. [ABSTRACT FROM AUTHOR]

The nonlinearity in Chua's oscillator is commonly implemented as a three-segment piecewise-linear resistor. The piecewise-linear nature of the element means that the implementation requires a significant amount of circuitry and the speed of operation is limited. The qualitative behavior of Chua's oscillator has also been captured using a smooth cubic nonlinearity; the implementation of the latter also requires a significant amount of circuitry and suffers from limited speed of operation. This work describes a novel implementation of Chua's oscillator using just four transistors and a battery to produce a cubic-like nonlinearity. The circuit is simple, robust, and capable of operating at frequencies over one thousand times greater than the original Chua's oscillator. [ABSTRACT FROM AUTHOR]