# user58533

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Trying to learn math :)

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 1d comment what are the equilibrium points of the following: I belive you should try it. Equilibria means "zero velocity" . Just solve the equations $12-3xy-3x=0$ and $3xy-6y=0$. Then try to interprete the result. 1d revised Find values of the parameters in Predator prey model added 869 characters in body Apr11 answered Help Finding Saddle Connections of a System Apr11 revised 2nd order linear differential equation added 117 characters in body Apr11 answered 2nd order linear differential equation Apr10 comment Principal direction in Dynamical System Indeed, you could translate principal direction as the direction of the eigenvector. The term "eigen" is german, however it is widely used I guess in many languages. Apr10 revised Find values of the parameters in Predator prey model added 11 characters in body Apr10 answered Find values of the parameters in Predator prey model Apr8 comment Uniqueness of solution to differential equation Fixed point theorem together with the assumption that the right hand side of the ODE is Lipschitz should be useful. Mar26 comment Can one exchange fibre and base space in a fibre bundle? @EarthliĆ : Did you find an answer to this? I am also very interested in such a thing. Mar19 awarded Scholar Mar19 accepted Center manifold of sets of equilibria Mar19 asked Help understanding a theorem on Lagrangians and extremals Mar18 comment Bifurcation in coupled differential equations Bifurcations normally have to do with parameters. When such parameters make the spectrum of a system cross the imaginary axis, then it is said that a bifurcation occurs. I do not think the definition of a bifurcation is only that 1 or more eigenvalues are 0. Your plot might be correct with the system, but something is missing to be able to talk of bifurcations. More precisely there is a $1$-dimensional center manifold (a local invariant) that contains the non-hyperbolic equilibrium point $(x,y)=(0,11)$ Mar18 comment Linear Differential Equation with Quasiperiodic Coefficient: A Question I am not expert but just from the sentence I guess there is a supposition (must probably quasi periodicity) that implies $\omega_i$ is irrational. Otherwise there exists an integer $A$ such that $A\omega_i=\omega_j$, which would mean that $a(t)$ is periodic and not quasi periodic (as stated in the hypothesis). Mar18 comment Principal direction in Dynamical System What are your thoughts? The fixed points are those $x$ where $F(x)=0$. At each fixed point $x^*$ you can compute the linear part $J=\partial F/\partial x (x^*)$. Such matrix $J$ gives a lot of information on the local behaviour of the solutions, provided $J$ is not too degenerate. The eigenvalues and eigenvectors of $J$ are very important to understand the solutions $x(t)$ "very" near the equilibrium points. Mar18 answered Topological conjugation between two flows Mar12 comment Reference request: Nonlinear dynamics graduate reference I would add the book Geometric theory of dynamical systems by Palis and de Melo, and maybe Dynamical Systems and chaos by Broer and Takens. There are plenty of references of a graduate level, but dynamical systems (in particular nonlinear dynamics) is a very broad topic. There is the encyclopaedia of dynamical systems as well (by V.I. Arnold), which treats many nonlinear phenomena in a rigorous way. Another applied mathematics book would be Nonlinear Differential Equations by Jordan and Smith. Mar11 answered Consider the system $x'= \frac{-x}{2}; y' = 2y + x^2$ to solve the system and find topologically conjugacy and show topologically conjugate Mar7 comment Find a nonlinear system conjugate the linear system $\overrightarrow x' = \left(\begin{array}{cc} 1 & 2\\0&-4 \end{array}\right) \overrightarrow x$. I think you are looking for the Hartman-Grobman theorem. In such case any nonlinear vector field with the linear part you wrote answers your question.