This work presents the Church thesis, its proof, and the notion of stability and stabilization for analog algorithms. The Church thesis for discrete algorithms motivates us to consider the Church thesis for the case when we are dealing with analog algorithms. Its presentation and proof follows a similar construction to the one given for discrete algorithms. The notions of analog algorithm and dynamical system are postulated to be equivalent. The stability and stabilization concepts for analog algorithms are defined. The stability and stabilization presentation starts concentrating in continuous and discrete dynamical systems i.e., analog algorithms, described by differential or difference equations and continues considering Lyapunov energy functions.

%V 23 %P 16 %8 12/2018 %G eng %U https://acadsol.eu/en/articles/23/2/1.pdf %N 2 %& 233 %R 10.12732/caa.v23i2.1 %0 Journal Article %J Communications in Applied Analysis %D 2018 %T MODELLING AND VERIFICATION ANALYSIS OF THE BIOLOGICAL INTERACTION BETWEEN SPECIES VIA A MODAL LOGIC APPROACH %A ZVI RETCHKIMAN KÖNIGSBERG %K 08A99 %K 39A11 %K 93D35 %K 93D99 %XThis paper addresses the interactions, among organisms of the same or different species associated with the need for a common resource that occurs in a limited supply relative to demand. If two competitors try to occupy the same realized niche, one species will try to eliminate the other. Therefore, two cases are worth to be considered. On the one hand, there is a need to cooperate sharing part of the resource so that both organisms will benefit from it. On the other hand, if one of the two species is stronger than the other, there will be no cooperation and the strongest species will impose its conditions. In the study of this interaction Lotka-Volterra models have been used. Other non-classical methodologies as Petri nets and first order logic have been employed too. In this work, the biological competition problem between species is modelled as a modal logic formula. Then, using the concept of logic implication, and transforming this logical implication relation into a set of clauses, a modal resolution qualitative method for verification (satisfiability) as well as performance issues, for some queries is applied.

%B Communications in Applied Analysis %V 22 %P 14 %8 07/2018 %G eng %U https://acadsol.eu/en/articles/22/3/8.pdf %N 3 %9 scientific: mathematics %& 459 %R 10.12732/caa.v22i3.8 %0 Journal Article %D 2017 %T MODELLING AND VERIFICATION ANALYSIS OF THE BIOLOGICAL COOPERATIVE COMPETITION PROBLEM VIA A FIRST ORDER LOGIC APPROACH %A ZVI RETCHKIMAN KÖNIGSBERG %K 08A99 %K 39A11 %K 93D35 %K 93D99 %XThis paper addresses the biological cooperative competition problem among organisms of the same or different species associated with the need for a common resource that occurs in a limited supply relative to demand. If two competitors try to occupy the same realized niche, one species will try to eliminate the other. Therefore, there is a need to cooperate sharing part of the resource so that both organisms will benefit from it. In this work, the biological cooperative competition problem is modelled as a formula of the first order logic. Then, using the concept of logic implication, and transforming this logical implication relation into a set of clauses, called Skolem standard form, qualitative methods for verification as well as performance issues, for some queries, are applied.

%V 21 %P 16 %8 04/2017 %G eng %U http://www.acadsol.eu/en/articles/21/3/2.pdf %N 3 %9 scientific: mathematics %! Biological Cooperative Competition Problem %& 337 %R 10.12732/caa.v21i3.2