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A method to calculate period doubling bifurcation
Applied Mathematics and Mechanics (English Edition), 1987This paper considers small periodic perturbations of second order nonlinear Duffing type equations. It is concerned with the phenomenon known as ``period doubling bifurcation'' interpreted as the combination of two unperturbed equation, whose periods are close to the period of the perturbation.
Liu, Zhengrong +2 more
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Quadratic stabilization of systems with period doubling bifurcation
Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2004In this paper we study the stabilization of discrete-time controlled dynamics with periodic doubling bifurcation using quadratic normal forms, centre manifold techniques and quadratic feedbacks. The procedure for designing a quadratic controller is also proposed.
Hamzi B. +2 more
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An Experimental Approach To Period Doubling Bifurcation In Plasmas
2017 IEEE International Conference on Plasma Science (ICOPS), 2017A direct current (dc) driven semiconductor-gas discharge system is designed to study nonlinear behavior and period doubling features experimentally. Numerical analysis and theoretical studies show that the period doubling is expected in the discharge 1.
Uzun Kaymak, İlker Ümit +1 more
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Dynamic period–doubling bifurcations of a unimodal map
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Davies, H. G., Rangavajhula, K.
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Property of period-doubling bifurcations
Chaos, Solitons & Fractals, 2005This paper considers an \(n\)-dimensional ordinary differential equation in the form of \(n\) relations giving the derivative of the phase vector with respect to the time. This equation depends on a parameter vector and is nonautonomous, i.e., the functions defining the right part of the \(n\) relations depend on the time.
Xu, M, Wang, L
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A universality of period doubling bifurcations
Physica D: Nonlinear Phenomena, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arimitsu, T., Motoike, T.
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A quasi-analytical method for period-doubling bifurcation
ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196), 2002Prediction of period-doubling bifurcation is accomplished very accurately by using higher-order Harmonic Balance Approximations (HBAs) and quasi-analytical monodromy-matrix evaluation. Approximation error analysis is carried out for the computation. An accurate detection of first period-doubling bifurcation in Chua's circuit is demonstrated.
Daniel W. Berns +2 more
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Period-doubling bifurcations in stimulated Raman scattering
Physical Review A, 1987We have studied two aspects of chaotic behavior in stimulated Raman scattering. The route to chaos in this nonlinear optical process has been shown to be period-doubling bifurcations. The fractal dimension of the Raman strange attractor has been calculated for different values of damping of the Stokes mode.
, Nath, , Ray
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Period-doubling bifurcations in the presence of colored noise
Physical Review E, 1994We study the effects of colored noise on period-doubling bifurcations. Using the Feigenbaum map as a model, the technique of cumulant equations is applied to analyze the bifurcation behavior. We find that the universal properties of the period-doubling sequences are preserved in the case of colored noise.
Neiman, A., Anishchenko, V., Kurths, J.
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Period-doubling bifurcations and chaos in an enzyme reaction
The Journal of Physical Chemistry, 1992The peroxidae-oxidase (PO) reaction is the peroxidase-catalyzed oxidation of organic electron donors with molecular oxygen as the oxidant. With NADH as the electron donor, the PO reaction is one of the simplest biochemical reactions showing nonlinear behavior such as bistability and oscillations.
Geest, Torben +3 more
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