6
votes
3answers
143 views
+200

Determining the maximum value for the solution of this delay differential equation?

I am working on the following delay differential equation $$\frac{df}{dt}=f-f^3-\alpha f(t-\delta)\tag{1},$$ where $\frac{1}{2}\leq\alpha\leq 1$ and $\delta\geq 1$. I know that there are three ...
0
votes
0answers
50 views

Is there a method to list all periodic points for a funcion?

I search for a method that finds all periodic points of a given function e.g. $f(x)=x-x^2$ on its domain. You may explain some methods for a part of functions e.g. polynomials or $\mathcal{C}^k$ or ...
0
votes
1answer
34 views

Periodic points of topologically conjugated functions in dynamical systems?

I'm working on a homework problem which seems obvious, but I am having a hard time proving/completing. The problem can be stated as follows: Let $f,g:$ $\mathbb R$ $\rightarrow$ $\mathbb R$ be ...
0
votes
1answer
56 views

Eventually periodic orbit?

I am doing a self study on dynamical systems. I faced the following exercise in this book: Prove that any point on $f:[0,1]\to [0,1],\ f(x)=3x \mod 1$ is eventually periodic iff its a rational ...
2
votes
1answer
91 views

Function from Cantor Set to itself.

I am stuck in getting rational functions (except identity) defined from Cantor set to itself. Please help me to get out these functions.
5
votes
1answer
124 views

Maps with every point being periodic

Does there exists a characterization of continuous maps $f:[0,1]\rightarrow [0,1]$ with every point $x\in [0,1]$ being periodic (i.e. if for every $x\in [0,1]$ there exists $n\in\mathbb{N}$ such that ...
3
votes
1answer
133 views

There is non-trivial function satisfy the given condition?

Let $f:[0,1]\to\Bbb{R}$ to be a function satisfying that $$ f(x)=\begin{cases} \frac{f(2x)}{2} &\text{if }x<1/2 \\ \frac{f(2x-1)}{2}+\frac{1}{2} & \text{if } x\ge1/2\end{cases} \qquad ...
0
votes
1answer
61 views

Continuum limit of cellular automata

Is there any function defined for say the plane, that has interesting nontrivial behaviour similar to Conway's Game Of Life, but where every point's on/off status is decided by something like the ...
2
votes
0answers
83 views

Cellular automata – like functions

Let's consider one dimensional cellular automaton. It is build upon its rule, i.e. a function $f : S^3 \rightarrow S$, where $S = \{0,1\}$. The case described is the elementary cellular automaton, ...