# dynamical

1. ### Basin of Attraction: Dynamical Systems

I'm supposed to use the Liapunov function (1/2)x^2 + (1/4)y^2=1/9 to verify that this ellipse is included in the basin of attraction of (0,0) of the system. x'= -x + y^2 y'= -2y + 3x^2 Can someone please see if I did this correctly?
2. ### Topology equivalence in dynamical system

Hi, my name is Eric. I've got trouble when proofing that system \dot{x}=\alpha+x^2+O(x^3) is topological equivalence with system \dot{x}=\alpha+x^2. I don't understand how to build the homeomorphism for the orbit. In literature, I read that for \alpha>0, the homeomorphism mapping is defined by...
3. ### Discrete-Time Dynamical Systems problem involving Equilibrium

I have been struggling with this problem for some time now, and I do not know how to approach it. Could anyone start me off? Thanks! Consider the alcohol consumption model: a/subscript: t+1/ = a/subscript: t/ - (10.1a/subscript: t/ divided by 4.2 + a/subscript: t/) + d, where d is the...
4. ### Classification of fixed points of N-dimensional linear dynamical system?

I'm familiar with the classification of fixed points of linear dynamical systems in two dimensions; it's readily available in many a book, as well as good ol' Wiki (Linear dynamical system - Wikipedia, the free encyclopedia). However, what happens with higher-order systems, say...
5. ### Chaos and Dynamical Systems

The equation P_n_+_1 = rP_n(1-P_n/C) -k may be considered a density - dependent population model with constant harvesting. If the growth rate is r = 3 and the carrying capacity is C = 6000, what is the largest number k that could be harvested each generation so that the population has a stable...
6. ### Dynamical system

a) Let f: S^1 -> S^1 be conjugated to an irratonal rotation. Show that the congujacy is unique up to rotation, i.e, if h1 and h2 are two conjugacies then h1 = R_alpha o h2, for some alpha. b)Show that tere are no expansive homeomorphism in S^1 (Hint: consider the rational, and irrational...
7. ### Dynamical systems

Suppose that y' = ay - H y(0) = y0, models a fish population where a and H are positive constants and 0 <y0 < H/a. Find the time t* when the population dies out. [Hint: set y = 0 in solution formula (9) and solve for t.] The solution formula, which I have confirmed both algebraically and...
8. ### Problems with Continuous Dynamical Systems

Hi there, I'm new to this but I was wondering if you could help me with my understanding of Dynamical Systems. I have a continuous dynamical system given by the equations: dx1/dt = x1(x2-x3) dx2/dt = x2(x3-x1) dx3/dt = x3(x1-x3) Which I need to analyse. There are a few problems I have but the...
9. ### Rotation of spiralling solution associate with complex eigenvalue of dynamical system

Hi, name is Eric. I'm a student in Indonesian university studying dynamical system. I'd like to ask sth concerning continuous dynamical system. If i have a planar autonomous or nonautonomous system, and the eigenvalue of the linearisation of the system is complex. Do the spiral of the solution...
10. ### Nonhomogenous dynamical systems

Find the general solution to the following: A(n+1)=2A(n)+3^n-n and find the particular solution when A(0)=1. I have like ten problems this way. After all my calulations i got A(k)=c2^k-3^k+k is this right? I'm lost on how to find the particular solution. Can anyone help?
11. ### link between stationary processes and dynamical systems

hi to everybody, Could someone explain me what is the exact difference between a stationary process in probability and a process arising from a dynamical system, say an observable computed along a discrete orbit? Suppose the existence of an invariant measure for the dynamical system built...
12. ### Pointers for Dynamical systems based ODE

Hi fellas, I'm new to the forum - found it in a bid to help seek pointers for maths assignments (not particularly good with the subject, but having to take it up as it replaced the original subject at my institute) Any pointers, tips would be appreciated thanks.
13. ### Two Dimensional Discrete Dynamical System

Hi, I have the following dynamical system, x_{n+1}={x_n}^2-{y_n}^2+a y_{n+1}=2x_ny_n Where a is real. And I am asked to consider the set of points on a circle of radius r and centre origin and show that they are mapped to another circle under one iteration. How do I go about...
14. ### Need help - difference equation / dynamical system / fixed points

I checked this forum for any potential help with dynamical systems/fixed points. I hope there is anybody who could help me with a couple of homework questions/tasks. I would very much appreciate any help and would also be willing to compensate. I need to provide solutions for the...
15. ### Dynamical Systems

Hey all, This is like pre differential equations aka dynamical systems. Here is the problem: You plan to invest part of your paycheck to finance your childrens education. you want to have enough in the account to draww \$1000 a month every month for eight years beginning twenty years from now...
16. ### Updating function problem. What is the solution of the dynamical system at x0=200?

xn+1= 0.85xn+75 explain thanks
17. ### Dynamical Systems

Hi, I am studying dynam systems and have missed some classes and am not sure if i'm on the right track or not, Dynamical system; dx/dt = rx - ( x/(1 + (x^2))) when asked to calc the fixed points for this system i figured to set the RHS to equal 0 and solve for x which gave me; x = (+/-)...
18. ### Dynamical Systems

I have a continuous dynamical system given by dx/dt = x(y-z), dy/dt = y(z-x) dz/dt = z(x-y) and have to show that for any initial condition x0 , y0 , z0 such that x0 +y0+z0= k for any constant k the solution of the above equations will always lie in the plane x+y+z=k...
19. ### dynamical system

hey, can anybody help? i have a 1 dimensional dynamical system in which x is greater than 0 x(with a dot on top)=f(x)=1-(5x^2)+(4x^4) how to i solve f(x*)=0 and find its fixed points? thanks
20. ### Dynamical system

I'm given F' = 0.01F(10-F-3R) R' = 0.0125R(8-R-2F) F' = 0.1F(1 - F/10) - 0.03FR R' = .1R (1 - R/8) - 0.025FR I have to find the four equilibrium points for the system. I'm a little confused about how to do this so if anyone could be of assistance, I would REALLY appreciate it!