Limit Cycles

Limit Cycles

An attractor for non-linear dynamic systems which has periodic cycles or orbits in phase space. An example is an undamped pendulum which will have a closed circle orbit equal to the amplitude of the pendulum's swing. See: Attractor, Phase Space.
References in periodicals archive ?
Van der Pol found stable oscillations, now known as limit cycles, in electrical circuits employing vacuum tubes.
Let us now analytically study the amplitude of the limit cycle by using the average method [13].
Our second main result states that when [DELTA] < 2, only fixed points can occur as limit cycles.
Phase plane is a direct method refers graphically to determine the existence of limit cycles in place the system behavior over the entire plane can be visualized and limit cycles can be easily identified [16].
Goldwyn and Cox (1965) used Lyapunov theory to generate unstable limit cycles as the boundary of a stable equilibrium.
ij]} the manifold on which the corresponding maps f have a center at the origin and to investigate the limit cycles bifurcations of such maps.
Langford's fundamental work in the field, the topics here include flow invariant subspaces for lattice dynamical systems, low- to high-dimensional behavior in waves in extended systems, mixed mode oscillations due to the generalized Canard phenomenon, bioremediation of waste in a porous medium, bifurcation of gyroscopic systems near a O:1 resonance, high dimensional data clustering from a dynamical systems point of view, and the computation of limit cycles as the second part of Hilbert's tenth problem.
In particular, [1] describes topics about limit cycles and some theorems of usefulness in typical specific nonlinear problems such as Vanderpol's equation.
In this case, however, various dynamic features are observed, including the limit cycles and the foci, which are not observed in the adiabatic systems.
2001) that the presence of stiction in control valve in a control loop produces limit cycles in the controlled variable (pv) and the controller output (op).
The authors describe their work in the existence and estimation of finite bounds for the number of limit cycles occurring in certain families of ordinary differential equations, and includes their methods such as bifurcation theory, asymtotic expansions, and methods of differential algebra.