- Tytuł:
- Periodic, nonperiodic, and chaotic solutions for a class of difference equations with negative feedback
- Autorzy:
- Kennedy, Benjamin B.
- Powiązania:
- https://bibliotekanauki.pl/articles/29519375.pdf
- Data publikacji:
- 2023
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
difference equation
negative feedback
circle map - Opis:
- We study the scalar difference equation $ x(k+1)=x(k)+\frac{f(x(k-N))}{N} $ where f is nonincreasing with negative feedback. This equation is a discretization of the well-studied differential delay equation $ x′(t) = f(x(t − 1)). $ We examine explicit families of such equations for which we can find, for infinitely many values of N and appropriate parameter values, various dynamical behaviors including periodic solutions with large numbers of sign changes per minimal period, solutions that do not converge to periodic solutions, and chaos. We contrast these behaviors with the dynamics of the limiting differential equation. Our primary tool is the analysis of return maps for the difference equations that are conjugate to continuous self-maps of the circle.
- Źródło:
-
Opuscula Mathematica; 2023, 43, 4; 507-546
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł