Memristor Based van der Pol Oscillation Circuit

Abstract

The memristor is referred to as the fourth fundamental passive circuit element of which inherent nonlinear properties offer to construct the chaos circuits. In this paper, a flux-controlled memristor circuit is developed, and then a van der Pol oscillator is implemented based on this new memristor circuit. The stability of the circuit, the occurring conditions of Hopf bifurcation and limit circle of the self-excited oscillation are analyzed; meanwhile, under the condition of the circuit with an external exciting source, the circuit exhibits a complicated nonlinear dynamic behavior, and chaos occurs within a certain parameter set. The memristor based van der Pol oscillator, furthermore, has been created by an analog circuit utilizing active elements, and there is a good agreement between the circuit responses and numerical simulations of the van der Pol equation. In the consequence, a new approach has been proposed to generate chaos within a nonautonomous circuit system. Int. J. Bifurcation Chaos 2014.24. Downloaded from www.worldscientific.com by UNIVERSIDAD POLITECNICA DE MADRID SERVICIO DE BIBLIOTECA UNIVERSITARIA on 01/05/15. For personal use only. Y. Lu et al. M (q) = dφ(q)/dq, where q(t) = t −∞ i(τ )dτ , φ(t) = 1450154-2 Int. J. Bifurcation Chaos 2014.24. Downloaded from www.worldscientific.com by UNIVERSIDAD POLITECNICA DE MADRID SERVICIO DE BIBLIOTECA UNIVERSITARIA on 01/05/15. For personal use only. Memristor Based van der Pol Oscillation Circuit 1450154-3 Int. J. Bifurcation Chaos 2014.24. Downloaded from www.worldscientific.com by UNIVERSIDAD POLITECNICA DE MADRID SERVICIO DE BIBLIOTECA UNIVERSITARIA on 01/05/15. For personal use only.

Prediction of period doubling bifurcations in harmonically forced memristor circuits

“…2. Table 1 reports the rational functions L i (D), i = 1, 2, 3, for some circuits which have been investigated in the literature (see, e.g., [34,36,[47][48][49], and references therein) 1 . For the circuit studied in [48], the rational function L 2 (D) is obtained once a real harmonic voltage input (u(t) + R s ) is connected in parallel to the memristor (cf.…”

A Chaotic Oscillator Based on HP Memristor Model

“…Applying an external sinusoidal excitation voltage to the autonomous system, a nonautonomous system is obtained, which is shown in Figure 4, where V( ) = sin(Ω ). Then (11) and (12) can be translated into (13) and 14, respectively; those are…”

“…Then some memristor oscillators with a PWL nonlinearity or a smooth piecewise-quadratic nonlinearity are presented based on Chua's circuit [11,12]. Meanwhile, some other memristor oscillators based on Chua's circuit are proposed, using diverse memristor models with the -nonlinearities: ( ) = + 3 [13]. In these studies, some new properties, which are different from conventional chaos, such as equilibrium set, transient chaos, and stable chaos with an intermittence period, are found.…”

“…On the other hand, a few nonautonomous memristor oscillators are proposed. In [13], an oscillation circuit based on van der Pol circuit oscillator is implemented. Very recently, nonautonomous Chua's circuit is constructed by replacing Chua's diode with a memristor model characterized by the memductance ( ) = − + | ( )|, which can exhibit some complex dynamical properties including transient chaos, transient hyperchaos, and chaotic beats [14].…”

A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

“…In recent years, generation and nonlinear analyses of memristor-based chaotic systems have attracted more and more attention, and become a research hotspot. By replacing Chua's diodes with memristors, adding memristors to existing nonlinear systems, and designing new systems with memristors, some new chaotic and hyperchaotic systems have been constructed, such as a memristor-based Chua's circuit [1][2][3][4][5][6], memristor-based van der Pol oscillator [7], memristor-based Lorenz system [8][9][10], memristor-based Chen system [11], memristor-based Lü system [12], etc. Theoretical analyses, numerical simulations and circuit experiments consistently indicate that such memristor-based systems can exhibit complex dynamical behaviours including various bifurcation [1][2][3][4][5][6][7][8][9][10][11][12], chaos [1][2][3][4][5][6][7][8][9][10][11][12], hyperchaos [12][13][14], coexistence of attractors [15], transient dynamical behaviors [16], and initial state dependent dynamical behaviors [17].…”