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This paper studies dynamics of a modulation-doped GaAs/AlGaAs heterostructure under transverse magnetic fields and microwave radiations. It finds that negative differential conductivity, due to the real-space electron transfer and delayed dielectric relaxation of the interface potential barrier, can lead to complex behaviours when a relatively small magnetic field is applied. Quasiperiodicity, frequency-locking and the routes from period-doubling to chaos are found. Under a large magnetic field, however, two time-independent homogeneous steady states exist; and the longitudinal resistance of the system shows an interesting oscillation with period tuned by the ratio of microwave radiation frequency ω to the cyclotron frequency ωc and local minima at ω/ωc = integer + 1/4.

With a simple piecewise-linear mode, this paper describes the nonlinear dynamics and its control of the Colpitts oscillator. An active control method is applied to guiding the design of the controllers to synchronize and anti-synchronize two identical Colpitts oscillators. And a sufficient condition is drawn for the stability of the error dynamics. Finally, numerical simulations show the effectiveness of the proposed control strategy.

From modern control theory, an active control method to synchronize two modified Chua circuits with each other, which exhibit chaos, is presented. Some sufficient conditions of linear stability of the chaotic synchronization are obtained from rigorous mathematic justification. On the basis of the state-observer, the controller is analytically deduced using the active control. It is shown that this technique can be applied to achieve synchronization of the two systems with each other, whether they are identical or not. Finally, numerical simulations show the effectiveness of the proposed control scheme.

This paper describes the method of synchronizing slave to the master trajectory using an intermittent state observer by constructing a synchronizer which drives the response system globally tracing the driving system asymptotically. It has been shown from the theory of synchronization error-analysis that a satisfactory result of chaos synchronization is expected under an appropriate intermittent period and state observer. Compared with continuous control method, the proposed intermittent method can target the desired orbit more efficiently. The application of the method is demonstrated on the hyperchaotic Rossler systems. Numerical simulations show that the length of the synchronization interval τs is of crucial importance for our scheme and the method is robust with respect to parameter mismatch.

We propose a method for laser cooling two-valence-electron fermionic atoms. Our protocol employs resolved-sideband cooling on the stimulated Raman transition between the two magnetic sublevels (m = F and m = F − 1) of the ground state with total angular momentum F. The optical pumping from m = F − 1 to 1P1 are used to decouple atoms in the m = F − 1 state. We calculate the Raman coupling generated by an engineered optical lattice. The result shows that it is possible to laser cool the two-valence-electron fermionic atoms to the ground state. The atoms in the ground state provide a new system for quantum optics.

By designing an appropriate state observer, we have constructed two subsystems which alternately synchronize the chaotic drive system. When the parameter of the transmitter is modulated using the binary digital signal, the two systems can alternately be synchronized with the chaotic system. In the receiver, information is demodulated by analyzing synchronization error. An observer-based parameter modulation and demodulation Henon system was chosen to be a typical example. Numerical simulation is carried out to illustrate the effectiveness and efficiency of the proposed method.

Synchronization of two chaotic systems with different parameters using the random parametric adaptive control algorithm is proposed. Under the appropriate control law and feedback coefficient, the synchronization is achieved. To make this method realizable, Henon map is taken as a typical numerical example. The characteristic of random control period and flexible feedback coefficient shows its practicality.

This paper develops a modified state observer for chaotic generalized synchronization. An analytic approach is proposed for constructing a response system to implement generalized chaos synchronization with drive system. From the state observer theory, some sufficient conditions of global asymptotic linear-generalized synchronization between the drive system and response system are obtained. Finally, a hyperchaotic R?ssler system is given to illustrate the effectiveness of the proposed synchronization method.

We develop the physical model based on the real space charge transfer mechanism and derive the dynamic equations of GaAs/AlGaAs heterostructures. Complex bifurcations are studied in detail for the forced and unforced cases. It is shown that both periodic attractors and fixed points attractors can coexist under a right dc bias. The hysteresis phenomena are also investigated in theory. For the forced GaAs/AlGaAs, numerical simulation shows that the occurance of frequency-locking, quasiperiodicity, and chaos depends on the frequency and amplitude of the externally applied microwave field, as expected.

This paper proposes an approach to control chaos based on occasional linear feedback.This scheme is composed of control and non-control phases.The different stable periodic orbits are obtained by adjusting the feedback coefficients and the time duration which the control phase occupies.We also simulate acousto-optic bistable model and Henon-like attactor.The results from the numerical simulation show that the method can switch effectively the system to the desired periodic orbits.

We present a method for the computation of Lyapunov exponents without reorthogon alization. In the low dimension of system(n