To better understand how the transition to chaos
happens, one may consider a so-called bifurcation diagram.
Reichl, The Transition to Chaos
in Conservative Classical Systems: Quantum Manifestations, Springer Verlag, New York, NY, USA, 1992.
Szabelski, "Transition to chaos
in the self-excited system with a cubic double well potential and parametric forcing," Chaos, Solitons & amp; Fractals, vol.
The muscular fibers of the heart may be regarded as a set of harmoniously pulsating oscillators, and the cardiac fibrillation preceding a cardiac collapse may be considered as a transition to chaos of the heart.
 Javier Montenegro Joo, (2009) Transition to chaos in the damped & forced non-linear oscillator.
For a better clarity, the transition to chaos
through the numerical simulation is shown for three values of [f.sub.p] = 0.3, [f.sub.p] = 0.38, and [f.sub.p] = 0.45 (see Figures 4 and 5).
Several routes to chaos have been observed, however, the Period Doubling Route to Chaos (PDRC) [8, 9] is a universal and fundamental form of transition from periodicity to chaos (Transition to chaos ), observed in many mathematical and real systems.
In the Transition to Chaos , a system evolves toward non periodic time dependence as one or more parameters are varied.
Now researchers have turned up theoretical and experimental evidence suggesting that this phase transition from an ordered to a disordered state may be an example of a transition to chaos
. In other words, the complicated motion of the ions in the disordered state, rather than being truly random and unpredictable, is deterministic.
The purpose of the investigation here reported has been to And out what happens beyond chaos in a non-linear forced and damped oscillator in which the transition to chaos
had previously been studied in up to one million time-steps [4,5,6].
Several routes to chaos have been observed, however, the Period Doubling Route to Chaos [4-5] is a universal and fundamental form of transition from periodicity to chaos (Transition to chaos
), observed in many mathematical and real systems.
While studying the transition to chaos
in the damped non-linear forced oscillator, this author observed that its route to chaos resembles the steps followed by a machine when it is on the verge of collapsing, and that chaos, this is the absence of a frequency, when the period becomes infinite (1-3), may be paralleled to machine collapse.