Multistability analysis and nonlinear vibration for generator set in series hybrid electric vehicle through electromechanical coupling

Nonlinear dynamics of a single-gap terahertz split-ring resonator under electromagnetic radiation

Research into metasurfaces is developing rapidly and is topical due to their importance and applications in various fields such as communications, cryptography, and sensing, to name a few. These materials are artificially engineered to manipulate/control electromagnetic (EM) waves, in order to present a particular functionality. In this regard, nonlinear metasurfaces may present particular functionalities that remain to be discovered. In this paper, we numerically investigate the dynamic behaviors caused by the motion of charge carriers under the intense EM field at the gap of a single nonlinear split-ring resonator (NSRR) in the terahertz (THz) frequency range. We derive the mathematical model that is used to examine the excitation properties of the NSRR and then demonstrate various tuning regions. Analysis of the two-dimensional parameter space reveals that the NSRR exhibits periodic, chaotic patterns as the amplitude of the excitation field and the loss parameter vary. However, this chaotic behavior disappears when the loss parameter is very large. The period doubling that confirms the transition between the periodic and chaotic modes is explored using the bifurcation diagram. The sensitivity of the initial conditions is examined on three dynamic region plots. Our results correctly demonstrate that the NSRR exhibits the attractive phenomenon of multistability. The coexistence of two stable states is studied and confirmed on the basin of attractions for a fixed set of amplitude or loss parameters. The energy balance of the proposed model is well analyzed on the dynamic states and parameters to characterize the different oscillation regimes. The study of the multistability in the work represents an important first step toward the development of photonic memory devices in the THz frequency range.

Nonlinear dynamics of discontinuous uncertain oscillators with unilateral constraints

Nonlinear dynamics of discontinuous oscillators with unilateral constraints and non-random parametric uncertainties are investigated. Nonlinear oscillators considering single- and double-sided constraints are carefully constructed to exhibit rich bifurcations, such as period-doubling and Neimark-Sacker bifurcations. In deterministic amplitude-frequency responses, both hardening and softening effects are induced by non-smooth contact-type nonlinearities. Stabilities of the solutions are determined by the shooting method and the monodromy matrix. To effectively quantify the behaviors of nonlinear oscillators in the presence of parametric uncertainties, a non-intrusive surrogate function aided by arc-length ratio interpolation is constructed. Simulation results demonstrate variabilities of nonlinear responses under different non-random uncertainties. Moreover, an accuracy verification is provided to verify the effectiveness of the non-intrusive uncertainty propagation method. It is found that the surrogate function in combination with the arc-length ratio technique has high accuracy and evolutions of turning points are captured satisfactorily regardless of complex interactions of nonlinearities and uncertainties. The findings and methodologies reported are meaningful to general nonlinear systems having complex motions, paving the road for more in-depth investigations into uncertain nonlinear dynamics.

A Chaotic Quadratic Oscillator with Only Squared Terms: Multistability, Impulsive Control, and Circuit Design

Here, a chaotic quadratic oscillator with only squared terms is proposed, which shows various dynamics. The oscillator has eight equilibrium points, and none of them is stable. Various bifurcation diagrams of the oscillator are investigated, and its Lyapunov exponents (LEs) are discussed. The multistability of the oscillator is discussed by plotting bifurcation diagrams with various initiation methods. The basin of attraction of the oscillator is discussed in two planes. Impulsive control is applied to the oscillator to control its chaotic dynamics. Additionally, the circuit is implemented to reveal its feasibility.

A new autonomous memristive megastable oscillator and its Hamiltonian-energy-dependent megastability

Multistability is a special issue in nonlinear dynamics. In this paper, a three-dimensional autonomous memristive chaotic system is presented, with interesting multiple coexisting attractors in a nested structure observed, which indicates the megastability. Furthermore, the extreme event is investigated by local riddled basins. Based on Helmholtz's theorem, the average Hamiltonian energy with respect to initial-dependent dynamics is calculated and the energy transition explains the occurrence mechanisms of the megastability and the extreme event. Finally, by configuring initial conditions, multiple coexisting megastable attractors are captured in PSIM simulations and FPGA circuits, which validate the numerical results.