The phase-modulated logistic map.
We study the logistic mapping with the nonlinearity parameter varied through a delayed feedback mechanism. This history dependent modulation through a phaselike variable offers an enhanced possibility for stabilization of periodic dynamics. Study of the system as a function of nonlinearity and modulation parameters reveals new phenomena: In addition to period-doubling and tangent bifurcations, there can be bifurcations where the period increases by unity. These are extensions of crises that arise in nonlinear dynamical systems. Periodic orbits in this system can be systematized via the kneading theory, which in the present case extends the analysis of Metropolis, Stein, and Stein for unimodal maps.
Nandi
Amitabha
A
School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India.
Dutta
Debabrata
D
Bhattacharjee
Jayanta K
JK
Ramaswamy
Ramakrishna
R
D016015:Logistic Models; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D010825:Physics / Q000379:methods*; D013598:Systems Theory