Frequently Hypercyclic and Chaotic Behavior of Some First-Order Partial Differential Equation

Abstract

We study a particular first-order partial differential equation which arisen from a biologic model. We found that the solution semigroup of this partial differential equation is a frequently hypercyclic semigroup. Furthermore, we show that it satisfies the frequently hypercyclic criterion, and hence the solution semigroup is also a chaotic semigroup.

On Frequently Hypercyclic c-Distribution Cosine Functions in Frechet Spaces

“…On the other hand, the notion of a frequently hypercyclic strongly continuous semigroup on a separable Banach space was introduced by E. M. Mangino and A. Peris in 2011 ( [29]). Frequently hypercyclic translation semigroups on weighted function spaces were further investigated by E. M. Mangino and M. Murillo-Arcila in [30], while the frequent hypercyclity of semigroup solutions for first-order partial differential equations arising in mathematical biology was investigated by C.-H. Hung and Y.-H. Chang in [20]. Frequent hypercyclicity and various generalizations of this concept for single operators and semigroups of operators are still very active field of research, full of open unsolved problems.…”

Chaotic and hypercyclic properties of the quasi-linear Lasota equation

“…It is so-called Lasota equation, studied by many authors (see e.g., [3,4,6,8,14]). The history of the problem studied in this paper is rather long and there were several approaches to it.…”