Narrow Results

We study the control of spontaneous emission in four-level atomic system driven by two fields. We show that with the variation of dynamical variable, namely, Rabi frequency, a wide variety of spectral behavior can be obtained, including extreme spectral narrowing. In our system, the spectrum of the spontaneous emission is independent of the phase associated with microwave field.

A general algorithm is proposed for controlling the amplitude of limit cycle emerging from the Hopf bifurcation in a 3D nonlinear dynamic system using nonlinear state feedback. An expression of the curvature coefficient of limit cycle and an explicit control formula are derived by utilizing the center manifold theory and normal form reduction. The expression and formula present a convenient approach to obtain an effective analytical control and predict the amplitude of limit cycles. Three examples — the Langford, the Chen and the Chua systems — are used to illustrate the application of this control approach. The simulation results are presented to confirm the analytical predictions.

A general method is introduced for controlling the amplitude of the variables in chaotic systems by modifying the degree of one or more of the terms in the governing equations. The method is applied to the Sprott B system as an example to show its flexibility and generality. The method may introduce infinite lines of equilibrium points, which influence the dynamics in the neighborhood of the equilibria and reorganize the basins of attraction, altering the multistability. However, the isolated equilibrium points of the original system and their stability are retained with their basic properties. Electrical circuit implementation shows the convenience of amplitude control, and the resulting oscillations agree well with results from simulation.

A crisis of amplitude control can occur when a system is multistable. This paper proposes a new chaotic system with a line of equilibria to demonstrate the threat to amplitude control from multistability. The new symmetric system has two coefficients for amplitude control, one of which is a partial amplitude controller, while the other is a total amplitude controller that simultaneously controls the frequency. The amplitude parameter rescales the basins of attraction and triggers a state switch among different states resulting in a failure of amplitude control to the desired state.

Chaotic dynamical systems without fixed points are promising in the generation of pseudo-random sequences because orbits will not converge to a fixed point. In this class of systems there are no final fixed points, so the basin of attraction of a fixed point does not exist. The absence of fixed points makes it difficult to analyze the dynamics of the systems because a fixed point gives us a lot of information about the dynamics of the system. In addition, if there is an amplitude control parameter for the generated chaotic signals, the tolerance and adaptability are higher and better in the application process. In view of the aforementioned, in this paper, a novel class of discrete maps is presented and described by a kind of piecewise linear (PWL) maps. Necessary and sufficient conditions are given to guarantee that this class of discrete maps does not have any fixed point. Furthermore, we introduce families of these PWL discrete maps without fixed points that present positive Lyapunov exponents and have chaotic dynamics with amplitude control. From these families, we select one particular map, which is analyzed theoretically and proved to be chaotic in the sense of Devaney.

This paper proposes a simple ring memristive neural network (MNN) with self-connection, bidirectional connection and a single memristive synapse. Compared with some existing MNNs, the most distinctive feature of the proposed MNN is that it can generate heterogeneous coexisting attractors and large-scale amplitude control. Various kinds of heterogeneous coexisting attractors are numerically found in the MNN, including chaos with a stable point, chaos with a limit cycle, a limit cycle with a stable point. By increasing the parameter values, the chaotic variables of the MNN can be accordingly increased and their corresponding areas are extremely wide, yielding parameter-dependent large-scale amplitude control. A circuit implementation platform is established and the obtained results demonstrate its validity and reliability.

Many real-world systems are connected together, in natural and man-made networks. A complex-valued laser network can simulate the working mechanism of human brain. However, amplitude control of a complex-valued laser network is seldom studied. In this paper, a ring network of complex-valued Lorenz laser systems is investigated. The ring network exhibits complex dynamics including hyper-chaos, quasi-periodic orbits, and coexisting hyper-chaos. Three kinds of single-parameter oriented amplitude controls are realized with varying or unvarying Lyapunov exponents in the ring network. Meanwhile, a simple knob can realize the amplitude rescaling of hyper-chaotic signals, which reduces the cost of circuit implementation. Moreover, a criterion of chaotic complete synchronization among all the nodes is established for a network with strong coupling. For relatively weak coupling, quasi-periodic complete synchronization is found, and the performance of chaotic synchronization is studied in terms of the cross-correlation coefficient. It is moreover revealed that the improvement and trend of synchronization performance are robust to the parity of the number of nodes for the same-scale laser networks.

The U-shaped steel-concrete composite hollow waffle (CHW) floor is an innovative slender large-span floor composed of a thin slab and bidirectional orthogonal steel-concrete composite hollow beams. Large vibrations may occur under human excitations, and vibration guidelines for CHW floors are still lacking. Thus, this paper undertook a parametric and experimental study to explore the vibration performance of the CHW floors. First, the modal properties and vibration response under walking tests considering the varying frequencies and routes were obtained from the measurements, which validated the accuracy of the finite element analysis (FEA). Then, the influence of the structural parameters on the floor vibration was investigated by numerical modeling. The parametric study shows that the medium-sized long-span (MLS) (28m) CHW floors present the best vibration serviceability, the small-sized long-span (SLS) (14m) CHW floors vibrate substantially under walking excitation, and the large-sized long-span (LLS) (42m) CHW floors are vulnerable to resonance. Finally, this paper provides recommendations for design guidelines for CHW floors and indicates that controlling the span-to-height (SH) value and beam spacing (BS) at a small value are the most effective methods of vibration control.