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We have developed a stabilization method of quasi-periodicity based on a return map. The method is explained in the forced Van der Pol oscillator, and applied experimentally to a quasi-periodic output of a Q-switched Nd:YAG laser. Even though the attractors have no unstable periodic orbit, we were able to stabilize them to an arbitrarily chosen orbit by targeting the trajectory into it.

We investigate the origin of the transition inside the desynchronization state via phase jumps in coupled chaotic oscillators. We claim that the transition is governed by type-I intermittency in the presence of noise whose characteristic relation is $ \propto \exp(\alpha|\epsilon_t -\epsilon|^{3/2})$ for $\epsilon_t -\epsilon \propto (\epsilon_t -\epsilon)^{-1/2}$ for $\epsilon_t -\epsilon >0$, where $$ is the average length of the phase locking state and $\epsilon$ is the coupling strength. To justify our claim we obtain analytically the tangent point, the bifurcation point, and the return map which agree well with those of the numerical simulations., Comment: 11 pages, 4 figures

We investigate nonlinear dynamical behaviors of operational amplifiers. When the output terminal of an operational amplifier is connected to the inverting input terminal, the circuit exhibits period-doubling bifurcation, chaos, and periodic windows, depending on the voltages of the positive and the negative power supplies. We study these nonlinear dynamical characteristics of this electronic circuit experimentally.

We investigate the characteristic relations of type-II and -III intermittencies in the presence of noise. The theoretically predicted characteristic relation is that $〈\mathcal{l}〉\ensuremath{\sim}\mathrm{exp}{|\ensuremath{\epsilon}{|}^{2}}$ for a negative regime of \ensuremath{\epsilon} and $〈\mathcal{l}〉\ensuremath{\sim}{\ensuremath{\epsilon}}^{\ensuremath{-}\ensuremath{\nu}}$ for the positive regime of \ensuremath{\epsilon} $(1/2l~\ensuremath{\nu}l1),$ where $〈\mathcal{l}〉$ is the average laminar length and $(1+\ensuremath{\epsilon})$ is the slope of the local Poincar\'e map around the tangent point. We experimentally confirm these relations in a simple electronic circuit.

Using mutually coupled nonidentical continuous-wave Nd:YAG lasers, we experimentally confirmed the recently proposed transition route from phase synchronization to complete synchronization. As evidence of this transition we obtained the probability distribution of the intermittent synchronization time near the threshold of the complete synchronization transition.

We have observed various synchronous motions between laser spots of TEM10 mode in a diode laser pumped Nd:YAG laser. The dynamics of TEM10 mode develop from synchronous motion to anti-synchronous motion through intermittent jumps between the two motions as the pumping increases. We analyze the phenomena experimentally.

The general structure of two-dimensional intermittency is discussed. The structure of channel and the trajectory in the return map are compared with those of one-dimensional intermittency and the scaling relations are obtained according to the trajectory. We illustrate the temporal behavior and scaling relations in a coupled map. The numerical results agree well with the theoretical predication of approximately equal 1/sqrt[epsilon].

We analyze the bifurcation of an attractor in a system of multiplicatively coupled maps. It is shown that the phenomenon can be characterized by on-off intermittency and it is rigorously described by the on-off intermittency in the presence of noise through the concept of a virtually invariant manifold. Presenting numerical results which conform our claims, we elucidate the role of on-off intermittency in bifurcation phenomena.

Near a phase synchronization region, the phase difference of two coupled chaotic oscillators exhibits phase jumps. For an example, the coupled Rossler oscillators exhibit 2π jumps, which is explained by using a potential shape of the phase related with type-I intermittency in the presence of noise. But, in our study, the two coupled hyperRossler oscillators exhibit ±2π jumps, which can not be explained in the previous way. So we suggest a general method to analyze the phenomenon which uses the return map of the phase equation and present the scaling relation of the phase jumps by using the scaling properties of the laminar length of intermittency in the presence of noise.

Near the point of tangent bifurcation, the scaling properties of the laminar length of type-I intermittency are investigated in the presence of noise. Based on analytic and numerical studies, we show that the scaling relation of the laminar length is dramatically deformed from $\frac{1}{\sqrt{\epsilon}}$ for $\epsilon >0$ to $\exp\{\frac{1}{D}|\epsilon|^{3/2}\}$ for $\epsilon, Comment: 4 pages, 4 figures

We study the phase synchronization (PS) with type-II intermittency showing $\pm 2 \pi$ irregular phase jumping behavior before the PS transition occurs in a system of two coupled hyperchaotic R\"{o}ssler oscillators. The behavior is understood as a stochastic hopping of an overdamped particle in a potential which has $2 \pi$-periodic minima. We characterize it as type-II intermittency with external noise through the return map analysis. In $\epsilon_{t} < \epsilon < \epsilon_{c}$ (where $\epsilon_{t}$ is the bifurcation point of type-II intermittency and $\epsilon_{c}$ is the PS transition point in coupling strength parameter space), the average length of the time interval between two successive jumps follows $ \sim \exp(\mid\epsilon_{t} - \epsilon\mid^{2})$, which agrees well with the scaling law obtained from the Fokker-Planck equation., Comment: 5 pages, 5 figures

We experimentally stabilize a chaotic output of a diode-laser-pumped Nd:yttrium–aluminum–garnet laser by using oscillation quenching. When the chaotic laser is mutually coupled with a Rossler oscillator that is implemented by an electronic circuit, both chaotic systems are stabilized to steady states. We experimentally study the route to the steady states as the coupling strength increases, and numerically confirm the route by coupling Lorenz and Rossler oscillators mutually.