Related papers: A piecewise linear model of self-organized hierarc…
What basic processes generate hierarchy in a collective? The Bonabeau model provides us a simple mechanism based on randomness which develops self-organization through both winner/looser effects and relaxation process. A phase transition…
Agent-based models describing social interactions among individuals can help to better understand emerging macroscopic patterns in societies. One of the topics which is worth tackling is the formation of different kinds of hierarchies that…
In [N. A. Baas, Emergence, Hierarchies, and Hyper-structures, in C.G. Langton ed., Artificial Life III, Addison Wesley, 1994.] a general framework for the study of Emergence and hyper-structure was presented. This approach is mostly…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
We here present a fixed agents version of an original model of the emergence of hierarchies among social agents first introduced by Bonabeau \textit{et al}. Having interactions occurring on a social network rather than among 'walkers'…
The Bonabeau model is a competing model where agents fight to maintain or change their positions. Originally studied on a finite lattice, in this model, one agent is randomly selected to move to a neighboring site chosen at random. If the…
The hierarchical topology is a common property of many complex systems. Here we introduce a simple but generic model of hierarchy growth from the bottom to the top. Therein, two dynamical processes are accounted for: agent's promotions to…
The 1995 model of Bonabeau et al. explains the emergence of social hierarchies through randomness, but gives as many leaders as followers. A simple modification allows a more realistic asymmetry with much less leaders.
We propose a model to show the self-assembling of network-like structures between a set of nodes without using preexisting positional information or long-range attraction of the nodes. The model is based on Brownian agents that are capable…
We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking…
In this article we investigate the phase transition phenomena that occur in a model of self-organisation through body-attitude coordination. Here, the body-attitude of an agent is modelled by a rotation matrix in $\mathbb{R}^3$ as in…
In addition to the emergent complexity of patterns that appears when many agents come in interaction, it is also useful to characterize the dynamical processes that lead to their self-organization. A set of ergodic invariants is identified…
The smooth piecewise-linear models cover a wide range of applications nowadays. Basically, there are two classes of them: models are transitional or hyperbolic according to their behaviour at the phase-transition zones. This study explored…
Self-organization is a process where a stable pattern is formed by the cooperative behavior between parts of an initially disordered system without external control or influence. It has been introduced to multi-agent systems as an internal…
Autonomous shape and structure formation is an important problem in the domain of large-scale multi-agent systems. In this paper, we propose a 3D structure representation method and a distributed structure formation strategy where settled…
There are many significant applied contexts that require the solution of discontinuous optimization problems in finite dimensions. Yet these problems are very difficult, both computationally and analytically. With the functions being…
It is shown how piecewise differentiable functions $F: \mathbb R^n \mapsto \mathbb R^m $ that are defined by evaluation programs can be approximated locally by a piecewise linear model based on a pair of sample points $\check x$ and $\hat…
Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ODEs with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlases they may be…
Normal form theory is developed deeply for planar smooth systems but has few results for piecewise-smooth systems because difficulties arise from continuity of the near-identity transformation, which is constructed piecewise. In this paper,…
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…