Parametric Excitation and Evolutionary Dynamics
نویسندگان
چکیده
منابع مشابه
Parametric Excitation and Evolutionary Dynamics
Parametric excitation refers to dynamics problems in which the forcing function enters into the governing differential equation as a variable coefficient. Evolutionary dynamics refers to a mathematical model of natural selection (the “replicator” equation) which involves a combination of game theory and differential equations. In this paper we apply perturbation theory to investigate parametric...
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Consider a one-mass system with two degrees of freedom, nonlin-early coupled, with parametric excitation in one direction. Assuming the internal resonance 1:2 and parametric resonance 1:2 we derive conditions for stability of the trivial solution by using both the harmonic balance method and the normal form method of averaging. If the trivial solution becomes unstable a stable periodic solution...
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It is a rule of thumb that time delay tends to destabilize any dynamical system. This is not true, however, in the case of delayed oscillators, which serve as mechanical models for several surprising physical phenomena. Parametric excitation of oscillatory systems also exhibits stability properties sometimes defying our physical sense. The combination of the two effects leads to challenging tas...
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This paper involves the dynamics of a delay limit cycle oscillator being driven by a time-varying perturbation in the delay: _ x 1⁄4 x t TðtÞ ð Þ εx3 with delay TðtÞ 1⁄4 2þεkþε cos ωt. This delay is chosen to periodically cross the stability boundary for the x1⁄40 equilibrium in the constant-delay system. For most of parameter space, the system is non-resonant, leading to quasiperiodic behavior...
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ژورنال
عنوان ژورنال: Journal of Applied Mechanics
سال: 2013
ISSN: 0021-8936,1528-9036
DOI: 10.1115/1.4023473