in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least...

the limit cycle to disrupt the oscillation and form two saddle points. Blue sky catastrophe in which a limit cycle collides with a nonhyperbolic cycle. Global...

known as a type of limit cycle, in electrical circuits employing vacuum tubes. When these circuits are driven near the limit cycle, they become entrained...

about the dynamical system, the fixed point becomes a small-amplitude limit cycle as the parameter changes. A Hopf bifurcation is also known as a Poincaré–Andronov–Hopf...

variable n ( t ) {\displaystyle n(t)} , allowing one to visualize the limit cycle. However, one must be careful because this is an ad-hoc method of visualizing...

of the cubic nullcline, there is a limit cycle and an unstable clockwise spiral point. b = 1.25. The limit cycle still exists, but for a smaller interval...

clock, and the heartbeat while resting. The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated:...

said to be at equilibrium. fixed points periodic orbits limit cycles attractors In general, limits sets can be very complicated as in the case of strange...

initially. Instead, after sufficient time, the oscillations approach a limit cycle. The best-known example is the clock reaction, the Belousov–Zhabotinsky...

reduce a multi-dimensional dynamical equation describing a nonlinear limit cycle oscillator into a one-dimensional phase equation. Many phenomena in our...