43 citations · 84 across the 14 of their papers we have counts for
15 papers
The lamplighter group of rank two generated by a bireversible automaton
Elsayed Ahmed, Dmytro Savchuk
We construct a 4-state 2-letter bireversible automaton generating the lamplighter group of rank two. The action of the generators on the boundary of t…
Endomorphisms of regular rooted trees induced by the action of polynomials on the ring of -adic integers
Elsayed Ahmed, Dmytro Savchuk
We show that every polynomial in defines an endomorphism of the -ary rooted tree induced by its action on the ring of -adic integers. The section…
On Dynamical Cournot Game on a Graph
E. Ahmed, M. I. Shehata, H. A. A. El-Saka
Cournot dynamical game is studied on a graph. The stability of the system is studied. Prisoner's dilemma game is used to model natural gas transmission.
On Fractals and Fractional Calculus Motivated by Complex Systems
Awatif M. Shahin, Elsayed Ahmed, Ahmed S. Elgazzar +1
Complex systems (CS) are ubiquitous in nature. It is argued that fractional order (FO) calculus is more suitable to describe fractal systems. Motivated by the fractal space time th…
On differences between fractional and integer order differential equations for dynamical games
E. Ahmed, A. S. Elgazzar, M. I. Shehata
We argue that fractional order (FO) differential equations are more suitable to model complex adaptive systems (CAS). Hence they are applied in replicator equations for non-coopera…
Survival May Not be for the Fittest (Lessons from some TV games)
E. Ahmed, A. S. Hegazi
In this paper we argue that biological fitness is a multi-objective concept hence the statement "fittest" is inappropriate. The following statement is proposed "Survival is mostly…