What causes period-doubling bifurcation?
In dynamical systems theory, a period-doubling bifurcation occurs when a slight change in a system’s parameters causes a new periodic trajectory to emerge from an existing periodic trajectory—the new one having double the period of the original.
What is meant by period-doubling?
(physics) A characteristic of the transition of a system or process from regular motion to chaos, in which the period of one of its parameters is seen to double.
Is bifurcation periodic?
At the bifurcation point the period of the periodic orbit has grown to infinity and it has become a homoclinic orbit. After the bifurcation there is no longer a periodic orbit. Left panel: For small parameter values, there is a saddle point at the origin and a limit cycle in the first quadrant.
Who discovered doubling cascade?
The first is an individual period-doubling bifurcation. The second is an infinite collection of period doublings that are connected together by periodic orbits in a pattern called a cascade. It was first described by Myrberg and later in more detail by Feigenbaum.
Who invented logistic map?
Ricker in 1954 and detailed analytic studies of logistic maps beginning in the 1950s with Paul Stein and Stanislaw Ulam that the complicated properties of this type of map beyond simple oscillatory behavior were widely noted (Wolfram 2002, pp. 918-919).
How do you do bifurcation analysis?
All equations that have fold bifurcation can be transformed into one of these normal forms. dt = f(x, c) Assume x∗ is an equilibrium value and c∗ is a bifurcation value. (x∗,c∗) = 0. To anaylse the equilibrium and bifurcation point we need to analyse the normal form.
What causes bifurcation?
Global bifurcations occur when ‘larger’ invariant sets, such as periodic orbits, collide with equilibria. This causes changes in the topology of the trajectories in the phase space which cannot be confined to a small neighbourhood, as is the case with local bifurcations.