相关论文: Boolean Dynamics with Random Couplings
Boolean networks are discrete dynamical systems in which the state (zero or one) of each node is updated at each time t to a state determined by the states at time t-1 of those nodes that have links to it. When these systems are used to…
Boolean networks are discrete dynamical systems where each automaton has its own Boolean function for computing its state according to the configuration of the network. The updating mode then determines how the configuration of the network…
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be…
Boolean networks, widely used to model gene regulation, exhibit a phase transition between regimes in which small perturbations either die out or grow exponentially. We show and numerically verify that this phase transition in the dynamics…
This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex…
The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
Canalization of genetic regulatory networks has been argued to be favored by evolutionary processes due to the stability that it can confer to phenotype expression. We explore whether a significant amount of canalization and partial…
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean…
It is widely recognized that entanglement generation and dynamical chaos are intimately related in semiclassical models via the process of decoherence. In this work, we propose a unifying framework which directly connects the bipartite and…
The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…
We investigate Threshold Random Boolean Networks with $K = 2$ inputs per node, which are equivalent to Kauffman networks, with only part of the canalyzing functions as update functions. According to the simplest consideration these networks…
The dynamics of nonlocally coupled dissipative kicked rotors is rich and complex. In this study, we consider a network of rotors where each interacts equally with a certain range of its neighbors. We focus on the influence of the coupling…
We discuss a generalization of the dephasing-type spin-boson model in which N qubits are connected to K bosonic modes in an arbitrary way. The model can be solved exactly for any initial state and coupling type. We found that this leads to…
We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic.…
A Boolean network is a mapping $f :\{0,1\}^n \to \{0,1\}^n$, which can be used to model networks of $n$ interacting entities, each having a local Boolean state that evolves over time according to a deterministic function of the current…
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…
We investigate analytically and numerically the critical line in undirected random Boolean networks with arbitrary degree distributions, including scale-free topology of connections $P(k)\sim k^{-\gamma}$. We show that in infinite…
The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations.…
The critical Kauffman model with connectivity one is the simplest class of critical Boolean networks. Nevertheless, it exhibits intricate behavior at the boundary of order and chaos. We introduce a formalism for expressing the dynamics of…