Multistable dynamics and control of a new 4D memristive chaotic Sprott B system

This work proposes and investigates the dynamic behavior of a new memristive chaotic Sprott B system. One of the interesting features of this system is that it has a bias term that can adjust the symmetry of the proposed model, inducing both homogeneous and heterogeneous behaviors. Indeed, the introduced memristive system can turn from rotational symmetry (RS) to rotational symmetry broken (RSB) system in the presence or the absence of this bias term. In the RS system (i.e., absence of the bias term), pairs of symmetric attractors are formed, and the scenario of attractor merging is observed. Coexisting symmetric attractors and bifurcations with up to four solutions are perfectly investigated. In the RSB system (i.e., the bias term is non-zero), many interesting phenomena are demonstrated, including asymmetric attractors, coexisting asymmetric bifurcations, various types of coexisting asymmetric solutions, and period-doubling transition to chaos. We perfectly demonstrate that the new asymmetric/symmetric memristive system exhibits the exciting phenomenon of partial amplitude control (PAC) and offset boosting. Also, we show how it is possible to control the amplitude and the offset of the chaotic signals generated for some technological exploitation. Finally, coexisting solutions (i.e., multistability) found in the novel memristive system are further controlled based on a linear augmentation (LA) scheme. Our numerical findings demonstrated the effectiveness of the control technic through interior crisis, reverse period-doubling scenario, and symmetry restoring crisis. The coupled memristive system remains stable with its unique survived periodic attractor for higher values of the coupling strength

Parameter and initial offset boosting dynamics in two-memristor-based Colpitts system

In this paper, a five-dimensional (5-D) two-memristor-based Colpitts system is constructed by introducing two ideal memristors with cosine memductance into the classical three-dimensional (3-D) Colpitts oscillator model. The proposed memristive Colpitts system possesses a plane equilibrium set and their stabilities are periodically varied on the memristor initial plane. Moreover, the stability distribution patterns are evolved with the change of system control parameters. The parameter- and initial-dependent behaviors are investigated by employing several numerical methods. The numerically simulated results indicate that the system trajectories are confined by several unstable stability regions around the initiating point, leading to the generation of parameter and initial offset boosting dynamics. Furthermore, a dimensionality reduction model with determined equilibrium is formulated through integral transformation of state variables. The parameter and initial offset boosting dynamics is reconstituted theoretically and expounded numerically. Finally, circuit synthesis and PSIM (power simulation) simulations are carried out to validate the abovementioned dynamical behaviors