相关论文: Boolean Monomial Dynamical Systems
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy…
Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the…
Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…
We approximate a chain recurrent dynamical system by periodic dynamical systems. This is similar to the well known Bohr theorem on approximation of almost periodic functions by periodic functions.
We propose a solitonic dynamical system over finite fields that may be regarded as an analogue of the box-ball systems. The one-soliton solutions of the system, which have nested structures similar to fractals, are also proved. The…
In this work we study the Boolean Networks of different geometric shape and lattice organization. It was revealed that no only a spatial shape but also type of lattice are very important for definition of the structure-dynamics relation.…
This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…
Using monotonicity theory we investigate the continuous dependence on parameters for the discrete BVPs which can be written in a form of a nonlinear system.
Does the interaction graph of a finite dynamical system can force this system to have a "complex" dynamics ? In other words, given a finite interval of integers $A$, which are the signed digraphs $G$ such that every finite dynamical system…
In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary number (but finite) of dropping sections and approximating some continuous nonlinear function. Studying all possible local and…
Finite dynamical systems (e.g. Boolean networks and logical models) have been used in modeling biological systems to focus attention on the qualitative features of the system, such as the wiring diagram. Since the analysis of such systems…
Let $f:\mathcal{M}\rightarrow\mathcal{M}$ be a continuous map defined on a compact metric space $\mathcal{M}$. An open dynamical system introduces disjoint open balls centered at points in $\mathcal{M}$, and considers the trajectories of…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a Boolean function, depending on a selected subset of variables. Boolean networks have been widely…