Related papers: Analysis of attractor distances in Random Boolean …
The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related…
Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…
In this study, we propose a multi branched network approach to predict the dynamics of a physics attractor characterized by intricate and chaotic behavior. We introduce a unique neural network architecture comprised of Radial Basis Function…
Kauffman net is a dynamical system of logical variables receiving two random inputs and each randomly assigned a boolean function. We show that the attractor and transient lengths exhibit scaleless behavior with power-law distributions over…
This paper is concerned with the reduction of a noisy synchronous Boolean network to a coarse-grained Markov chain with number of states being equal to the number of attractors of the original network.
An account is given of the features, of the kind pertaining to q-statistics, of the dynamics at the one-dimensional critical attractors associated to the three familiar routes to chaos, intermittency, period doubling and quasiperiodicity.…
Characterization of the differences between biological and random networks can reveal the design principles that enable the robust realization of crucial biological functions including the establishment of different cell types. Previous…
Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…
A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time. These patterns are limit cycle…
We study the synchronization behavior of discrete-time Markov chains on countable state spaces. Representing a Markov chain in terms of a random dynamical system, which describes the collective dynamics of trajectories driven by the same…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
In systems biology, attractor landscape analysis of gene regulatory networks is recognized as a powerful computational tool for studying various cellular states from proliferation and differentiation to senescence and apoptosis. Therefore,…
We reduce complex stripped patterns to a basic topological network of edges and vertices to define defects and measure their influence on the pattern. We present statistics on the spatial and temporal distribution of defects within the…
The statistical properties of the length of the cycles and of the weights of the attraction basins in fully asymmetric neural networks (i.e. with completely uncorrelated synapses) are computed in the framework of the annealed approximation…
We study classes of dynamical systems that can be obtained by constructing recursive networks with monotone Boolean functions. Stack filters in nonlinear signal processing are special cases of such systems. We show an analytical connection…
A template describes the topological properties of a chaotic attractor. For attractors bounded by genus-1 torus, a linking matrix describes the topology of the template. It has been shown that the template depends on the Poincar\'e section…
The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the…
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We…
This study introduces an algorithm that generates undirected graphs with three main characteristics of real-world networks: scale-freeness, short distances between nodes (small-world phenomenon), and large clustering coefficients. The main…
During the last few years an area of active research in the field of complex systems is that of their information storing and processing abilities. Common opinion has it that the most interesting beaviour of these systems is found ``at the…