Questions tagged [bifurcation]

Question 1

My intuition for the answer is NO, here is my thought: Let $T(x,\lambda)$ be the map depending on one parameter $\lambda$, assume at $(x_0,\lambda_0)$ a tangent bifurcation occurs for the $T^2$ map, ...

Question 2

I am stuck in solving the following point of this exercise. We consider maps $f_\alpha:[−1,+1]\setminus\{0\}→[−1,+1]$, where $\alpha\in (1,2]$, given by $$f_\alpha(x)=\alpha x−\text{sign}(x)$$ where $\...

Question 3

Consider the 1-dimensional autonomous ODE \begin{align} \dot{x} = \mu + 2x^2 - x^4 \end{align} where $\mu \in \mathbb{R}$ is a parameter. I have found the fixed points, their stability, and plotted ...

Question 4

I have a 3d dynamical system that I am investigating that undergoes a series of bifurcations as two parameters ($I_1$ and $I_2$) are varied. The parameters represent input entering the system along ...

Question 5

I'm trying to study the behaviour of the family of maps $T_h:[0,1]\to[0,1]$ defined by $T_h(x)=\min{(h,1-2|x-\frac{1}{2}|)}$. I stumbled upon the family at the end of this paper on Sharkovsky's ...

Question 6

Based on the concept of logistic iterative operations, $x\rightarrow kx(1-x)$,where $k\in[0,4]$, I have proposed a similar iterative operation relationship.Specifically, I considered the form $${} x\...

Question 7

I have a system of differential equations with the following shape: $$ \dot{x} = ax + y $$ $$ \dot{y} = 2ax + 2y $$ I am trying to calculate where is the bifurcation of the system. I calculated the ...

Question 8

I am looking for a good reference on catastrophe theory or bifurcation theory for gradient flows defined by a time-dependent potential function, specifically of the form $\dot{x} = \nabla_x f(x, u)$ ...

Question 9

I wanted to ask the following question - Given a knot $K$, is there any algorithm, knot invariant, some heuristic (or anything really) which can tell if $K$ is a cable knot? The reason I am interested ...

Question 10

We are given the following dynamic system $$ \dot{x} = -a x + y + x(x^2 + y^2) - a \frac{x^2}{\sqrt{x^2 + y^2}} $$ $$ \dot{y} = -x - a y + y(x^2 + y^2) - a \frac{x^2 y}{\sqrt{x^2 + y^2}} $$ where $a $...

Question 11

I'm trying to find the points of the $(\alpha ,\beta )$-parameter space where the following system undergoes saddle-node bifurcation: $$ \dot{x}=y+\beta x+ x^2 $$ $$ \dot{y}=\alpha + x^2 $$ I've done ...

Question 12

Is there any possible way to write this differential equation (1) in terms of planar dynamical system variables? $\phi_{\xi \xi} = - \phi \frac{\phi_{\xi}^{2}(2 \phi^2 + 4 c) + (ck - \Omega^2) - 2 \...

Question 13

I am working with normal forms and encountered the following statement in a paper. The system $$ \left\{ \begin{array}{l} \dot{w}_0 = w_1 \\ \dot{w}_1 = a2 w_0^2 + b_2 w_0 w_1 + a_3 w_0^3 + b_3 w_0^2 ...

Question 14

The logistic map typically converges to a "carrying capacity", or output value across iterations, at r values (the growth rate) under 3. After 3, the value the system converges to bifurcates ...

Question 15

I am new to this knowledge. Here is the given scenario of the problem (please check the picture for clarification). Given a function $u'(t) = f(u;m)$, $t$ is time, $u$ is the enzyme concentration at ...

Stack Exchange Network

Questions tagged [bifurcation]

Can even periodic points of a map undergo tangent bifurcation?

Study of bifurcation [closed]

Types of bifurcations in $\dot{x} = \mu + 2x^2 - x^4$

3d-bifurcation classification

Family of truncated tent maps

Strange phenomenon in iterative operations

Bifurcation of a system of a parametric system of differential equations

Modern References on Catastrophe and Bifurcation Theory for Gradient Flows with Time-Dependent Potential

Detecting cable knots

Using Poincaré-Bendixson theorem to show closed trajectories

How to find the points of saddle-node bifurcation in a two-parameter dynamical system?

Is there any possible way to write this differential equation in terms of planar dynamical system variables?

Transforming Normal Forms via Smooth Coordinate Changes and Time Reparametrization

Why does the bifurcation diagram of the logistic map exhibit chaotic behavior past exactly r=3.57? What about 3.57 causes it to be the breaking point?

Bifurcation Diagram based on unknown function [closed]

Hot Network Questions