Dynamic Switching Networks (original) (raw)
Related papers
2013
Recent experiments have highlighted how collective dynamics in networks of brain regions affect behavior and cognitive function. In this paper we show that a simple, homogeneous system of densely connected oscillators representing the aggregate activity of local brain regions can exhibit a rich variety of dynamical patterns emerging via spontaneous breaking of permutation or translational symmetry. Our results connect recent experimental findings and suggest that a range of complicated activity patterns seen in the brain could be explained even without a full knowledge of its wiring diagram.
Self-organized pattern formation and noise-induced control based on particle computations
Journal of Statistical Mechanics: Theory and Experiment, 2005
We propose a new non-equilibrium model for spatial pattern formation based on local information transfer. Unlike most standard models of pattern formation it is not based on the Turing instability or initially laid down morphogen gradients. Information is transmitted through the system via particle-like excitations whose collective dynamics results in pattern formation and control. Here, a simple problem of domain formation is addressed by means of this model in an implementation as stochastic cellular automata, and then generalized to a system of coupled dynamical networks. One observes stable pattern formation, even in the presence of noise and cell flow. Noise contributes through the production of quasi-particles to de novo pattern formation as well as to robust control of the domain boundary position. Pattern proportions are scale independent as regards system size. The dynamics of pattern formation is stable over large parameter ranges, with a discontinuity at vanishing noise and a second-order phase transition at increased cell flow.
Turing patterns mediated by network topology in homogeneous active systems
Physical Review E
Mechanisms of pattern formation-of which the Turing instability is an archetype-constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing instability can induce pattern formation in discrete media such as complex networks, opening up the intriguing possibility of exploring it as a generative mechanism in a plethora of socioeconomic contexts. Yet, much remains to be understood in terms of the precise connection between network topology and its role in inducing the patterns. Here, we present a general mathematical description of a two-species reaction-diffusion process occurring on different flavors of network topology. The dynamical equations are of the predator-prey class, that while traditionally used to model species population, has also been used to model competition between antagonistic ideas in social systems. We demonstrate that the Turing instability can be induced in any network topology, by tuning the diffusion of the competing species, or by altering network connectivity. The extent to which the emergent patterns reflect topological properties is determined by a complex interplay between the diffusion coefficients and the localization properties of the eigenvectors of the graph Laplacian. We find that networks with large degree fluctuations tend to have stable patterns over the space of initial perturbations, whereas patterns in more homogenous networks are purely stochastic.
Steering complex networks toward desired dynamics
Scientific Reports, 2020
We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great practical interest in many areas of science, as well as providing insight into the interplay between network structure and dynamical behavior. We propose a pinning protocol for imposing specific dynamic evolutions compatible with the equations of motion on a networked system. The method does not impose any restrictions on the local dynamics, which may vary from node to node, nor on the interactions between nodes, which may adopt in principle any nonlinear mathematical form and be represented by weighted, directed or undirected links. We first explore our method on small synthetic networks of chaotic oscillators, which allows us to unveil a correlation between the ordered sequence of pinned nodes and their topological influence in the network. We then ...
Complex Networks from Simple Rules
Complex Systems, 2013
Complex networks are all around us, and they can be generated by simple mechanisms. Understanding what kinds of networks can be produced by following simple rules is therefore of great importance. This issue is investigated by studying the dynamics of extremely simple systems where a "writer" moves around a network, modifying it in a way that depends upon the writer's surroundings. Each vertex in the network has three edges incident upon it, which are colored red, blue, and green. This edge coloring is done to provide a way for the writer to orient its movement. The dynamics of a space of 3888 of these colored trinet automata systems are explored. A large variety of behavior is found, ranging from the very simple to the very complex. Our systems are studied using simulations (with appropriate visualization techniques) and selected rules are analyzed mathematically. An empirical classification scheme is arrived at, which reveals a lot about the kinds of dynamics and networks that can be generated by these systems.
Biological Pattern Generation: The Cellular and Computational Logic of Networks in Motion
Neuron, 2006
In 1900, Ramó n y Cajal advanced the neuron doctrine, defining the neuron as the fundamental signaling unit of the nervous system. Over a century later, neurobiologists address the circuit doctrine: the logic of the core units of neuronal circuitry that control animal behavior. These are circuits that can be called into action for perceptual, conceptual, and motor tasks, and we now need to understand whether there are coherent and overriding principles that govern the design and function of these modules. The discovery of central motor programs has provided crucial insight into the logic of one prototypic set of neural circuits: those that generate motor patterns. In this review, I discuss the mode of operation of these pattern generator networks and consider the neural mechanisms through which they are selected and activated. In addition, I will outline the utility of computational models in analysis of the dynamic actions of these motor networks.
Spontaneous structure formation in a network of dynamic elements
Physical Review E, 2003
As a model of temporally evolving networks, we consider a globally coupled logistic map with variable connection weights. The model exhibits self-organization of network structure, reflected by the collective behavior of units. Structural order emerges even without any interunit synchronization of dynamics. Within this structure, units spontaneously separate into two groups whose distinguishing feature is that the first group possesses many outwardly directed connections to the second group, while the second group possesses only a few outwardly directed connections to the first. The relevance of the results to structure formation in neural networks is briefly discussed.