Related papers: Exact dynamics of the critical Kauffman model with…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
There are insights of chaotic properties in economic systems and data. To prove the existence of chaotic dynamics, the establishment of a deterministic model is mandatory. A global modelling tool (GPoM) is used to search for mathematical…
In this paper, we propose an approach for modeling and analysis of a number of phenomena of collective behavior. By collectives we mean multi-agent systems that transition from one state to another at discrete moments of time. The behavior…
Boolean Networks (BNs) describe the time evolution of binary states using logic functions on the nodes of a network. They are fundamental models for complex discrete dynamical systems, with applications in various areas of science and…
We study the class of cooperative Boolean networks whose only regulatory functions are COPY, binary AND, and binary OR. We prove that for all sufficiently large N and c < 2 there exist Boolean networks in this class that have an attractor…
We prove that cooperativity in Boolean networks precludes a strong notion of sensitive dependence on initial conditions. Weaker notions of sensitive dependence are shown to be consistent with cooperativity, but if each regulatory functions…
Living systems operate in a critical dynamical regime -- between order and chaos -- where they are both resilient to perturbation, and flexible enough to evolve. To characterize such critical dynamics, the established 'structural theory' of…
Network structure strongly constrains the range of dynamic behaviors available to a complex system. These system dynamics can be classified based on their response to perturbations over time into two distinct regimes, ordered or chaotic,…
We explore the dynamical behavior at and near a special class of two-dimensional quantum critical points. Each is a conformal quantum critical point (CQCP), where in the scaling limit the equal-time correlators are those of a…
Networked systems display complex patterns of interactions between a large number of components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology,…
We study Boolean networks which are simple spatial models of the highly conserved Delta-Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in…
It is known that there are no more Lyndon words of length n than there are periodic necklaces of same length. This paper considers a similar problem where, additionally, the necklaces must be without some forbidden factors. This problem…
Unidirectionally coupled Lorenz systems in which the drive possesses a chaotic attractor and the response admits two stable equilibria in the absence of the driving is under investigation. It is found that double chaotic attractors coexist…
We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in…
An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and…
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…
Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switching between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering…
In previous works, we introduced the notion of dominant vertices in the context of dynamical systems on networks. This is a set of nodes in the underlying network whose evolution determines the whole network's dynamics after a transient…
There are three main aims of this paper. 1- I explain reasons why I await life to lie significantly deeper in chaos than Kauffman approach does, however still in boundary area near `the edge of chaos and order'. The role of negative…
We consider critical phenomena on heterogeneous small-world networks having a scale-free character but also arbitrary short-loops. After deriving the self-consistent equation for the order parameter and the critical surface, we prove that…