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Interpretation:
For the system, bifurcation occurs at the origin when
Concept Introduction:
Suppose we have a physical system that settles down to equilibrium through exponentially damped oscillations. Now suppose that the decay rate depends on a control parameter
A subcritical Hopf bifurcation occurs at
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Chapter 8 Solutions
Nonlinear Dynamics and Chaos
- The distances between Earth and nearby planets can be approximated using the phase angle α, as shown in the figure. Suppose that the distance between Earth and the sun is 93,000,000 miles and the distance between Venus and the sun is 67,000,000 miles. Approximate the distance between Earth and Venus to the nearest million miles when α = 34.arrow_forwardD7. Determine the oscillation of x²-x²+x + x = 0.arrow_forwardState the amplitude, period, phase shift and range for the sinusoid g(x) = -3sin(5x-11/4) + 19arrow_forward
- Find period, phase shift, domain and range of y=2sin1/4(x+π/4)-1arrow_forwardConsider the function f(x)=2sin(Pi/2(x-3))+4. State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0,P], State the maximum and minimum y-values and their corresponding x-valuesarrow_forwardEnter the equation of the function cos(x) that has a vertical shift of 4 units up, and a phase shift of π6 units right.arrow_forward
- What is the phase shift of the following graph? y = -4 sin( 7(x + 1)) O A. T ОВ. -4 ОС. 2 O D. -1arrow_forwardCompare the phase shift and amplitude of y=-cos(x-180∘) and y=-2sin(x-90∘). Which of the following choices is the correct comparison? a The cosine function has a phase shift that is 12 that of the sine function and in the same direction; the amplitude of the cosine function is 2 times that of the sine function. b The cosine function has a phase shift that is 12 that of the sine function and in the opposite direction; the amplitude of the cosine function is 12 that of the sine function. c The cosine function has a phase shift that is 2 times larger than the phase shift of the sine function and in the same direction; the amplitude of the cosine function is 12 that of the sine function. d The cosine function has a phase shift that is 2 times larger than that of the sine function and in the opposite direction; the amplitude of the cosine function is 2 times that of the sine function.arrow_forward1. y = -4Cos2x + 7 TC 2. y = 5Sin(÷x)+8 %3D | a. Amplitude= a. Amplitude= b. Frequency= b. Frequency= c. Period= c. Period= d. Y Max= d. Y Max= e. Y Minimum= e. Y Minimum=arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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