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Period-Doubling Bifurcations in Atomic Force Microscopy

Volume 6: ASME Power Transmission and Gearing Conference; 3rd International Conference on Micro- and Nanosystems; 11th International Conference on Advanced Vehicle and Tire Technologies, 2009
The dynamic response of an atomic force microscope cantilever probe is studied for off-resonance excitation and interactions with a soft silicone rubber material. The dynamic response of the probe is simulated using a three-mode approximation of the Euler-Bernoulli beam model for excitation at two-and-a-half times the probe’s fundamental frequency ...
Andrew J. Dick, Wei Huang
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Period-doubling bifurcations in the presence of colored noise

Physical Review E, 1994
We 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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Alternans and period-doubling bifurcations in atrioventricular nodal conduc

Journal of Theoretical Biology, 1995
A theoretical model, formulated as a finite difference equation is proposed for rate-dependent conduction properties of the atrioventricular (AV) node. The AV nodal conduction time, which is defined as the time interval from the atrial activation to the activation of the bundle of His, depends on the history of activation of the node.
J, Sun   +3 more
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Sinusoidally Varying Period-Doubling Bifurcations

1999
Bifurcations of dynamic systems may be affected in a variety of ways if the parameter that controls the bifurcation is varied slowly. The variation may alter, delay, or eliminate the bifurcation, introduce new types of bifurcation, or change stability regions. The variation may be imposed deliberately to control the response of the system.
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Period-doubling bifurcations and chaos in an enzyme reaction

The Journal of Physical Chemistry, 1992
The 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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Seasonality and period-doubling bifurcations in an epidemic model

Journal of Theoretical Biology, 1984
The annual incidence rates of some endemic infectious diseases are steady while others fluctuate dramatically, often in a regular cycle. In order to investigate the role of seasonality in driving cycles of recurrent epidemics, we analyze numerically the susceptible/exposed/infective/recovered (SEIR) epidemic model with seasonal transmission.
J L, Aron, I B, Schwartz
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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), 2002
Prediction 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.
D.W. Berns, J.L. Moiola, G. Chen
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Probability symmetry broken upon rapid period-doubling bifurcation

Technical Physics Letters, 2000
A quadratic one-dimensional mapping with noise is used to model the phenomenon of violation of the equal probability of variants in the postbifurcation system evolution upon a fast change of the control parameter. The case of a period-doubling bifurcation, after which only one of the two types of oscillations with different phases may occur in the ...
B. P. Bezruchko, R. N. Ivanov
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Generalized renormalization group equation for period-doubling bifurcations

Physics Letters A, 1984
Abstract Given a mapping x → ƒ(λ,x) , whose bifurcation points accumulate at λ = Λ∞, it is shown that the iterates (−α) p× [ƒ 2p (Λ ∞ −μ/δ p , X ∞ +y/(−α) p )−X ∞ ] converge to a function ψ(μ,y)asp→∞, where X∞ maximizes ƒ(Λ ∞,x ) .
K.L. Liu, W.S. Lo, K. Young
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Erratum: "A UNIVERSALITY OF PERIOD-DOUBLING BIFURCATIONS"

Modern Physics Letters B, 2000
T. ARIMITSU, T. MOTOIKE
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