This letter studies frequency-locked rotations in a phase-locked loop (PLL) circuit as FM demodulator. A rotation represents a desynchronized steady state in the PLL circuit and is regarded as another type of self-excited oscillations with natural rotation frequencies. The rotation frequency can be locked at driving frequencies of modulation signals. This letter shows response curves for harmonic amplitude of frequency-locked rotations. They have several different features from response curves of van der Pol oscillator.

In this paper, the stress wave propagation in a coupled pendulum system with friction force is discussed experimentally and numerically. The coupled system is analogous to the one dimensional fault dynamics model in seismicity. However, we will not intend to discuss about the geophysical feature of the system. The system has rich characteristics of the spatio-temporal stress wave propagation effected by nonlinear friction force. The relation between the wave propagation and the vibration of the pendulum is mainly discussed on the standpoint of nonlinear coupled system.

We report relations between invariant manifolds of saddle orbits (Lyapunov family) around a saddle-center equilibrium point and lowest periodic orbits on the two degree of freedom swing equation system. The system consists of two generators operating onto an infinite bus. In this system, a stable equilibrium point represents the normal operation state, and to understand its basin structure is important in connection with practical situations. The Lyapunov families appear under conservative conditions and their invariant manifolds constitute separatrices between trapped and divergent motions. These separatrices continuously deform and become basin boundaries, if changing the system to dissipative one, so that to investigate those manifolds is meaningful. While, in the field of two degree of freedom motions, systems with saddle loops to a saddle-center are well studied, and existence of transverse homoclinic structure of separatrix manifolds is reported. However our investigating system has no such loops. It is interesting what separatrix structure exists without trivial saddle loops. In this report, we focus on above invariant manifolds and lowest periodic orbits which are foliated for the Hamiltonian level.

Methods of automatically adjusting delay time and feedback gain in controlling chaos by delayed feedback control are proposed. These methods are based on a gradient-descent procedure minimizing the squared error between the current state and the delayed state. The method of adjusting delay time and that of adjusting feedback gain are applied to controlling chaos in numerical calculations of Rossler Equation and Duffing equation, respectively. Both methods are confirmed to be successful.

This paper demonstrates results of a numerical experiment on bifurcation phenomena in a two-degrees-of-freedom Duffing's type forced oscillatory system. The regions in the parameter plane (amplitude B and angular frequency ν of the external force) are given, in which various phenomena; chaos, hyperchaos, Hopf-bifurcations, doubling of torus, crisis and windows are observed. Existence of chaos and hyperchaos is confirmed by calculating the Lyapunov exponents. Bifurcations from invariant closed curves to chaotic attractors are also considered. For this system, two types of bifurcations from invariant closed curves to chaotic attractors through doubling of torus are observed; in one case, the doubling is interrupted by modelocking, then a chaotic attractor appears suddenly, in another case, the doubling seems to continue infinitely.

Spatiotemporal chaos in a multidomain regime in a Gunn-effect device is numerically investigated as an example of collective domain oscillations under global constraints. The dynamics of carrier densities are computed using a set of model partial differential equations. Numerical results reveal some distinctive and chaotic clustering features caused by the global coupling and boundary effects. The chaotic regime is then characterized in terms of a Lyapunov spectrum and Lyapunov dimension, the latter increasing with the size of the system.