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We review existing approaches to mathematical modeling and analysis of multi-agent systems in which complex collective behavior arises out of local interactions between many simple agents. Though the behavior of an individual agent can be…
We propose a Markov jump process with the three-state herding interaction. We see our approach as an agent-based model for the financial markets. Under certain assumptions this agent-based model can be related to the stochastic description…
Directed acyclic graphs (DAGs) are a popular framework to express multivariate probability distributions. Acyclic directed mixed graphs (ADMGs) are generalizations of DAGs that can succinctly capture much richer sets of conditional…
We develop a learning-based algorithm for the distributed formation control of networked multi-agent systems governed by unknown, nonlinear dynamics. Most existing algorithms either assume certain parametric forms for the unknown dynamic…
Evolution algebras are a new type of non-associative algebras which are inspired from biological phenomena. A special class of such algebras, called Markov evolution algebras, is strongly related to the theory of discrete time Markov…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
Agent-based modeling (ABM) offers powerful insights into complex systems, but its practical utility has been limited by computational constraints and simplistic agent behaviors, especially when simulating large populations. Recent…
We consider transformations between attractor basins of binary cylindrical cellular automata resulting from mutations. A t-point mutation of a state consists in toggling t sites in that state. Results of such mutations are described by a…
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…
Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
The continuous-time quantum walk on the underlying graphs of association schemes have been studied, via the algebraic combinatorics structures of association schemes, namely semi-simple modules of their Bose-Mesner and (reference state…
In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…
We study the dynamics of individual agents in some kinetic models of wealth exchange, particularly, the models with savings. For the model with uniform savings, agents perform simple random walks in the "wealth space". On the other hand, we…
State-space estimation and tracking rely on accurate dynamical models to perform well. However, obtaining an vaccurate dynamical model for complex scenarios or adapting to changes in the system poses challenges to the estimation process.…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied,…
Molecular dynamics simulations allow to study the structure and dynamics of single biomolecules in microscopic detail. However, many processes occur on time scales beyond the reach of fully atomistic simulations and require coarse-grained…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
This paper presents an analytical treatment of economic systems with an arbitrary number of agents that keeps track of the systems' interactions and agents' complexity. This formalism does not seek to aggregate agents. It rather replaces…