Find the equilibrium
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
Finite Mathematics (11th Edition)
- Sketch a graph of the updating function of the discrete-time dynamical system. Draw a cobwebbing diagram that determines whether the equilibrium point(s) are stable or unstable. (You will want to choose initial conditions near the equilibrium point(s), on each side, to check for stability.) Pt+1 = 0.6Pt + 0.8arrow_forwardPopulation equilibria can be stable or unstable. If, when a population deviates a bit from the equilibrium value (as populations inevitably do), it tends to return to it, this is a stable equilibrium; if, however, when the population deviates from the equilibrium it tends to diverge from it even further, this is an unstable equilibrium. Think of a ball in the pocket of a snooker table versus a ball balanced on a snooker cue. Unstable equilibria are a feature of Allee effect models such as the following. dN Use a phase portrait of the autonomous equation above to determine whether the nonzero equilibria that you found in question (2) are stable or unstable. (Hint: See Section 2.1 of the text. List the equilibria according to their stability. Enter your answers as comma-separated lists. If there are no equilibria in a certain category, enter NONE.) stable N = unstable N =arrow_forwardWhat is the equilibrium vector?arrow_forward
- (b): Find the steady state vector of the following regular matrix 0 0.2 0.0 0 0.3 0.3 1 0.5 0.7arrow_forwardFind the steady-state vector for the matrix below. 0.6 0.2 0.2 P = 0.2 0.6 0.2 0.2 0.2 0.6 q= -(Type an integer or simplified fraction for each matrix element.)arrow_forwardConsider the dynamical system Yk=1 = log (yk) + Yk- Which of the following statements is true about the dynamical system? O The dynamical system has infinite fixed points. The dynamical system has only one fixed points. The dynamical system has.no fixed points.arrow_forward
- where A = \-4 Find the state transition matrix of the following system: where A = [ 31 B = [ c = [0 1] -3. e(cos2t + sin2t) 2e-tsin2t e-tsin2t e-'(cos2t – sin2t) Ob. -e-tsin2t [e-t(cos2t + sin2t) -2e-tsin2t e-(cos2t – sin2t). c. -e-lsin2t [e-t(cos2t + sin2t) 2e-tsin2t e-t(cos2t – sin2t). d. (cos2t + sin2t) e-tsin2t (cos2t + sin2t) e-tsin2t -2e-tsin2t e-(cos2t – sin2t)l -2e-tsin2t e-(cos2t – sin2t)l CLEAR MY CHOICEarrow_forwardConsider a dynamical system given by Xn+1 = ,which one of the following is X11? X11 = X11 = X11 = X11 = [a(1.09)" b(0.91)" [a(0.91) b(1.09)". [a(0.91)¹1 b(1.09)11 [a(1.09)11- b(0.91)¹1 0.91 0 0 1.09 Xn. Assuming that Xo = a barrow_forwardConsider the discrete-time dynamical system modeling the concentration of a chemical in a lung. (Note: round all values at the end of the calculations and use 4 decimal places.) ct+1 = (1 - p)ct + pβ Let V = 2 L, W = 1 L, and β = 6 mmol/L If c0 = 7 mmol/L, iterate to find the following values: c1 = ____mmol/Lc2 = ____mmol/Lc3 = ____mmol/Lc4 = ____mmol/Larrow_forward
- The matrix that projects onto the line y = 2 -x is 0.599 0.800 0.800 -0.599arrow_forwardConsider a dynamical system given by Xn+1 ,which one of the following is X11? X11 = X11 = X11 = X11 = [a(1.09)” b(0.91)" [a(0.91)¹1 [b(1.09)¹¹ [a(1.09)11- b(0.91)11 [a(0.91)n [6(1.09)" = [0.91 0 0 1.09 Xn. Assuming that x = a [9]arrow_forward...*..****..........*...........*............. ....*.........................* ......... 0 0 1 The eigenvalues of the matrix 00 0 are: 0 0 Select one: a. 0,0,0 b. -2,1,1 c. 0,1,-1 d. 0,1,1arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning