Parallel and sequential dynamics of two discrete models of signed integer partitions

Chiaselotti, Giampiero; Gentile, Tommaso; Oliverio, Paolo Antonio

doi:10.1016/j.amc.2014.01.118

Cited by 16 publications

(9 citation statements)

References 14 publications

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“…Network models are the natural way to formalize the evolution of any phenomenon that includes cells, gens, entities, or any kind of distinct elements which interact among them. Thus, it is not amazing the big amount of papers, published in the last decades, associated with sciences (see, for instance, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]) and engineering (see, for instance, [19][20][21][22][23][24]), where such models appear to represent different phenomena and study their behavior.…”

Section: Introductionmentioning

confidence: 99%

Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems

et al. 2019

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Section: Introductionmentioning

confidence: 99%

Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems

et al. 2019

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“…Besides, in [53], a class of lattices and Boolean functions are employed to study the truth of a mathematical conjecture. Other related interesting works in this research line are [54][55][56][57].…”

Section: Introductionmentioning

confidence: 98%

Parallel Dynamical Systems over Graphs and Related Topics: A Survey

Aledo¹,

Martinez²,

Valverde

2015

Journal of Applied Mathematics

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In discrete processes, as computational or genetic ones, there are many entities and each entity has a state at a given time. The update of states of the entities constitutes an evolution in time of the system, that is, a discrete dynamical system. The relations among entities are usually represented by a graph. The update of the states is determined by the relations of the entities and some local functions which together constitute (global) evolution operator of the dynamical system. If the states of the entities are updated in a synchronous manner, the system is called aparallel dynamical system. This paper is devoted to review the main results on the dynamical behavior of parallel dynamical systems over graphs which constitute a generic tool for modeling discrete processes.

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“…Examples of such systems include deterministic networks models, logical models, agent-based models, Petri nets, and finite state machines. Indeed, these kinds of systems have been used to model natural events such as gene regulatory networks [1][2][3][4][5][6], and processes coming from computer sciences [7,8], chemistry [9,10], physics [11][12][13][14], biology [15,16], and social sciences [17]. Although these systems can be simulated on a computer, only a few analytical results beyond simulation are available.…”

Section: Introductionmentioning

confidence: 99%

On the Periodic Structure of Parallel Dynamical Systems on Generalized Independent Boolean Functions

et al. 2020

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In this paper, based on previous results on AND-OR parallel dynamical systems over directed graphs, we give a more general pattern of local functions that also provides fixed point systems. Moreover, by considering independent sets, this pattern is also generalized to get systems in which periodic orbits are only fixed points or 2-periodic orbits. The results obtained are also applicable to homogeneous systems. On the other hand, we study the periodic structure of parallel dynamical systems given by the composition of two parallel systems, which are conjugate under an invertible map in which the inverse is equal to the original map. This allows us to prove that the composition of any parallel system on a maxterm (or minterm) Boolean function and its conjugate one by means of the complement map is a fixed point system, when the associated graph is undirected. However, when the associated graph is directed, we demonstrate that the corresponding composition may have points of any period, even if we restrict ourselves to the simplest maxterm OR and the simplest minterm AND. In spite of this general situation, we prove that, when the associated digraph is acyclic, the composition of OR and AND is a fixed point system.

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Parallel and sequential dynamics of two discrete models of signed integer partitions

Cited by 16 publications

References 14 publications

Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems

Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems

Parallel Dynamical Systems over Graphs and Related Topics: A Survey

On the Periodic Structure of Parallel Dynamical Systems on Generalized Independent Boolean Functions

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