Related papers: An Analytical Framework to Describe the Interactio…
Complementarity is one of the main features underlying the interactions in biological and biochemical systems. Inspired by those systems we propose a model for the dynamical evolution of a system composed by agents that interact due to…
One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact…
Can one demonstrate quantitative effects of diversity within a system comprised of distinct individuals on the performance of the system as a whole? Assuming that individuals can be different, we develop a model to interpolate between…
Drawing on the understanding of the logistic map, we propose a simple predator-prey model where predators and prey adapt to each other, leading to the co-evolution of the system. The special dynamics observed in periodic windows contribute…
We review a body of recent work by the author and collaborators on controlling the spatial organisation of large agent populations across multiple scales. A central theme is the systematic bridging of microscopic agent-level dynamics and…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated…
In the paper, a linear differential equation with variable coefficients and a Caputo fractional derivative is considered. For this equation, a Cauchy problem is studied, when an initial condition is given at an intermediate point that does…
Bounded-confidence models in social dynamics describe multi-agent systems, where each individual interacts only locally with others. Several models are written as systems of ordinary differential equations with discontinuous right-hand…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…
We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their…
A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…
Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…
This article studies the Cauchy problem for the scalar conservation law \[ \partial_t u + \partial_t w + \partial_x f(u) = 0, \] where $w(x,t) = [\mathcal{F}(u)(x,t)]$ is the output of a specific hysteresis operator, namely the Play…
The paper entitled "Well posedness of general cross-diffusion systems", by C. Choquet, C. Rosier, L. Rosier, J. Diff. Eq. 2021, is devoted to the mathematical analysis of the Cauchy problem for general cross-diffusion systems without any…
We consider the Cauchy problem for a second-order evolution equation, in which the problem operator is the sum of two self-adjoint operators. The main feature of the problem is that one of the operators is represented in the form of the…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
We propose a method to systematically represent both the static and the dynamic components of environments, i.e. objects and agents, as well as the changes that are happening in the environment, i.e. the actions and skills performed by…
We consider the problem of solving a linear system of equations which involves complex variables and their conjugates. We characterize when it reduces to a complex linear system, that is, a system involving only complex variables (and not…
This paper introduces a novel reachability problem for the scenario involving two agents, where one agent follows another agent using a feedback strategy. The geometry of the reachable set for an agent, termed \emph{dependent reachable…