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(6 points) The point (-1,1) is a critical point of the nonlinear system of equations This critical point is a(n) (a...
The system results from an approximation to the Hodgkin-Huxley equations, which model the transmission of neural impulses along an axon. (a) Determine all critical points of the given system of equations. [Write your points in ascending order of their x-coordinates.] (___, ___) (___, ___) (___, ___) (b) Classify the critical points by investigating the approximate linear system near each one. **Choose one of the 3 in the () to fill in the blank** The critical point is _______(a saddle, a...
4. (-/2 points) DETAILS Classify the critical point (0, 0) of the given linear system by computing the tracer and determinant A and using the figure. x - 4x + 3y y' - 2x - 7y A4 Stable spiral 12.44 Unstable spiral Stable node Unstable node 72-44 <0 Center Degenerate stable node Degenerate unstable node Saddle stable spiral degenerate stable node unstable spiral О О О О О О О saddle center stable node unstable node degenerate unstable node
Classify (if possible) each critical point of the given plane autonomous system as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Order your answers from smallest to largest x, then from smallest to largest y.) x' = xy - 3y - 4 y' = y2 - x2 Conclusion (x, y) =( stable spiral point (x, y) =( unstable spiral point
please give specific steps of all the questions, thanks Q1. The following nonlinear system of DE's can be interpreted as describing the inter- action of two species with population densities r and y, respectively. 1dy1 2dt 2 dt (a) Write the given system in the form where A is a matrix with constant enteries. Also, show that the system is locally linear. (b) This system has three equilibrium or critical points. Determine those critical points and give a physical interpretation...
I'm completely stumped on these. I don't know how to proceed once I get to the eigenvalue since my typical method for solving would be to set Ax=x , then solve. However, this would give me -5x1=-5x1 and -5x2=-5x2 which makes A trivial. I just realized that means the eigenvectors will be <1,0> and <0,1>, but I'm still stumped on parts b and c. Consider the following system. (A computer algebra system is recommended.) dx = -5 0x dt *...
dx Consider the system 2 - NICO ху 2 22 dy dt = 2y – 1- 2XY dt 2 (a) Identify all critical points of the system. (b) For each critical point, use eigenvalues to classify the critical points according to stability (stable, unstable, asymptotically stable) and type (saddle, proper node, etc).
please show steps. Classify (if possible) each critical point of the given plane autonomous system as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Order your answers from smallest to largest x, then from smallest to largest y.) Conclusion ...Select (X, Y) - ( (x, y) - ( ) ) --Select --Select Slot Need Help? Read it TH
Classify (if possible) each critical point of the given plane autonomous system as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Order your answers from smallest to largest x, then from smallest to largest y.) x' = x(1 - x? - 9y2 y' y(9-x -9y?) Conclusion Select ---Select- (x, y) = --- Select (x, y) = -Select- ---Select
(1 point) a. Find the most general real-valued solution to the linear system of differential equations a' 2.(0) z(t) C + c b. In the phase plane, this system is best described as a O source / unstable node sink/stable node O saddle O center point/ ellipses spiral source Ospiral sink
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit in absence of species r? (c) Find all critical (equilibrium) points d) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point. (e)...