Observation of many bifurcation sequences in a driven piecewise-linear circuit

Dynamics of a nearly symmetrical piecewise linear oscillator close to grazing incidence: Modelling and experimental verification

“…The simplest case, and the one which has received most attention in the literature, is a one degree-of-freedom (1DOF) system with one or more symmetrical piecewise smooth characteristics under harmonic excitation. Physical examples of piecewise systems include a flexible ball bouncing on a hard surface [1], switching in electrical circuits [2], an oscillator making intermittent contact with one or two secondary springs [3][4][5][6], and systems with piecewise damping [7]. The extreme cases where the primary stiffness is zero, the so-called dead zone restoring force, have also been studied, e.g.…”

Controlling of Chaos in the Driven Chua's Circuit

“…From this figure one can easily identify the regions of period-doubling bifurcations, windows, period-adding sequences and boundary region. [12][13][14] Also, equal periodic bifurcations, intermittent transitions, hysteresis and coexistence of multiple attractors have been observed. Table 1 briefly summarizes some of the results of this circuit for certain parameters.…”

“…[6][7][8][9][10][11] Recently, we have initiated a study of the nonautonomous version of Chua's circuit under the influence of an external periodic signal. [12][13][14] To start with we have reported the effect of the periodic forcing on the fixed point attractor for certain circuit parameters. We have shown that as the forcing parameters are varied, the system enters into a complicated dynamics, through period-doubling bifurcations, chaos, equal periodic bifurcation, intermittency, period adding sequences and so on 12-14 j n a su b se q Ueri t study, we have reported the influence of the periodic signal on the familiar double-scroll chaotic attractor of Chua's circuit leading to a quasiperiodic route to chaos and devil's staircase structures.…”

Sliding Bifurcations in the Memristive Murali-Lakshmanan-Chua Circuit and the Memristive Driven Chua Oscillator

“…In this section, we describe the dynamics of a driven memristive Chua's circuit. This circuit itself is obtained by modifying the driven Chua's circuit, a fourth order non-autonomous circuit first introduced by Murali and Lakshmanan in the year 1990 [Murali & Lakshmanan, 1990]. The reason for selecting this circuit is that it is found to exhibit a large variety of bifurcations such as period adding, quasi-periodicity, intermittency, equal periodic bifurcations, re-emergence of double hook and double scroll attractors, hysteresis and coexistence of multiple attractors, besides the standard bifurcations.…”

“…The reason for selecting this circuit is that it is found to exhibit a large variety of bifurcations such as period adding, quasi-periodicity, intermittency, equal periodic bifurcations, re-emergence of double hook and double scroll attractors, hysteresis and coexistence of multiple attractors, besides the standard bifurcations. Its dynamics in the environment of a sinusoidal excitation has been extensively studied in a series of works by Murali and Lakshmanan [Murali & Lakshmanan, 1990;Lakshmanan & Murali, 1991;Murali & Lakshmanan, 1992a,c,b]. Due to its simplicity and the rich content of its nonlinear dynamical phenomena, the driven Chua's circuit continues to evoke renewed interest by researchers in the field of non-linear electronics [Anishchenko et al, 1993;Zhu & Liu, 1997;Elwakil, 2002;Srinivasan et al, 2009] The driven memristive Chua's circuit is obtained by replacing the Chua's diode in the original driven Chua's circuit with the active flux controlled active memristor introduced by the authors in 2011, as its nonlinearity.…”