Concept explainers
Interpretation:
To find the value of
Concept Introduction:
A fixed point of a differential equation is a point where
Holonomic bifurcation is the infinite period bifurcation in which limit cycle moves closer and closer to the saddle point, and at the bifurcation, cycle touches the saddle point and becomes a holonomic orbit.
Phase portraits represent the trajectories of the system with respect to the parameters and give a qualitative idea about the evolution of the system, its fixed points, whether they will attract or repel the flow, etc.
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Check out a sample textbook solutionChapter 8 Solutions
Nonlinear Dynamics and Chaos
- YOUR TURN Consider the system of differential equations dx1dt=x1x23x1dx2dt=3x1x26x2 a. Find all equilibrium points. b. Sketch a phase plane diagram, similar to Figure 11.arrow_forwardcharacterize the equilibrium point for the system x′= Ax and sketch the phase portrait.arrow_forwardSolve using the integrating factor by inspection (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0 Where y=1 when x=3arrow_forward
- Consider the system dx/dt = x(2-x-y) dy/dt = y(y-x2) a. Determine and sketch the nullclines. b. sketch the phase portrait and briefly describe the behavior of solutions.arrow_forwardAnalyze the dynamics of the system x' = y, y' = -x(1x) + cy for different positive values of c. Draw phase diagrams for each case, illustrating the behavior.arrow_forwardSolve the system dx/dt=2x-y, dy/dt=x Solve by systematic eliminationarrow_forward
- Find the solution. (dy/dx) + xy = xy³ Ax=(ce-²-1) 2 B y = (ce¹ +1) y = (ce x²-1) (ce²+1) X = D NÍZ 2 - 2arrow_forwardsolve linear DE (D2+2D+2)y=e-x+sin2xarrow_forwardState whether the equation is ordinary or partial, linear or non-linear and give its order. Ordinary or Linear or Non- Equation Order Partial linear dy = cos x dx džy + k²y = 0 dx2 (x² + y²)dx – 2xydy = 0 1 2 3 (a²u a²u\ = h? əx² ` əy², 4 du at 5 d²i di +R dt +i = Ew cos wt dt2 a2v = 0 əx² ay² 7 (d²w\ dw - xy + w = 0 dx dx² d³x dy d²y dx2 8 dx +x 4xy = 0 dy +7 dx, - 8y = 0 af af nf ду 10 axarrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,