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Three problems of resonance in coupl...

Lazarus, Lauren.

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Three problems of resonance in coupled or driven oscillator systems.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Three problems of resonance in coupled or driven oscillator systems./
作者:	Lazarus, Lauren.
面頁冊數:	83 p.
附註:	Source: Dissertation Abstracts International, Volume: 77-08(E), Section: B.
Contained By:	Dissertation Abstracts International77-08B(E).
標題:	Applied mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10036969
ISBN:	9781339547077

Three problems of resonance in coupled or driven oscillator systems.
Lazarus, Lauren.

Three problems of resonance in coupled or driven oscillator systems. - 83 p.

Source: Dissertation Abstracts International, Volume: 77-08(E), Section: B.

Thesis (Ph.D.)--Cornell University, 2016.

The behaviors of three oscillator systems with various types of coupling or driving terms are discussed, with particular regard to their resonance patterns.

ISBN: 9781339547077Subjects--Topical Terms:

2122814
Applied mathematics.

Three problems of resonance in coupled or driven oscillator systems.
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100 1 $a Lazarus, Lauren. $3 3192640
245 1 0 $a Three problems of resonance in coupled or driven oscillator systems.
300 $a 83 p.
500 $a Source: Dissertation Abstracts International, Volume: 77-08(E), Section: B.
500 $a Adviser: Richard H. Rand.
502 $a Thesis (Ph.D.)--Cornell University, 2016.
520 $a The behaviors of three oscillator systems with various types of coupling or driving terms are discussed, with particular regard to their resonance patterns.
520 $a In our first problem, a pair of phase-only oscillators are coupled to each other and driven by a third oscillator. By considering the phase differences between each oscillator and the driver, we find the region of parameter space where the system is entrained to the frequency of the driver. A complete analytical equation and multiple approximations for the boundary of this region are discussed. Additionally, the region where the oscillators "drift" relative to the driver is explored by using numerical methods. We find various m:n resonances between the oscillators within this region.
520 $a Our second and third problems involve a first-order delay differential equation where the system is found to oscillate provided the delay is greater than a critical value.
520 $a In the second problem, two identical delay limit cycle oscillators are coupled via instantaneous linear terms. This system has two invariant manifolds corresponding to in-phase and out-of-phase motions. Behavior on each manifold is expressed as a single delay limit cycle oscillator with an instantaneous self-feedback term. The strength of this self-feedback term changes the critical delay value needed for the system to oscillate. If strong enough, it also creates additional equilibrium solutions and can even prevent the system from oscillating in a stable way for any amount of delay.
520 $a The third problem explores parametric excitation of the delay limit cycle oscillator, by adding a sinusoidal time-varying driving term as a perturbation to the delay value. For most parameter values, this term is non-resonant and causes the system to exhibit quasiperiodic behavior. However, using a two-variable expansion perturbation method, we find a 2:1 resonance between the frequency of the driving term and the natural frequency of the unperturbed oscillator. Expanding about this resonance by a combination of analytical and numerical methods reveals a variety of local and global bifurcations forming the transition between resonant and non-resonant behaviors. The corresponding regions of parameter space are found to hold multiple stable and unstable steady-states.
590 $a School code: 0058.
650 4 $a Applied mathematics. $3 2122814
650 4 $a Mechanics. $3 525881
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710 2 $a Cornell University. $3 530586
773 0 $t Dissertation Abstracts International $g 77-08B(E).
790 $a 0058
791 $a Ph.D.
792 $a 2016
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10036969