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A class of hyperbolic reaction--diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and…
Hyperbolic transport-reaction equations are abundant in the description of movement of motile organisms. Here, we focus on system of four coupled transport-reaction equations that arises from an age-structuring of a species of turning…
In this work we review a class of deterministic nonlinear models for the propagation of infectious diseases over contact networks with strongly-connected topologies. We consider network models for susceptible-infected (SI),…
The methodology named LIFE (Linear-in-Flux-Expressions) was developed with the purpose of simulating and analyzing large metabolic systems. With LIFE, the number of model parameters is reduced by accounting for correlations among the…
Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this…
Kato's theory on the construction of strongly continuous evolution systems associated with hyperbolic equations is applied to the linear equation describing an age-structured population that is subject to time-dependent diffusion. The…
In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish…
Motivated by three recent open questions in the study of linear dynamics, we study weighted shifts on sequence spaces. First, we provide an example of a weighted shift on a locally convex space whose topology is generated by a sequence of…
We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…
This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…
These lecture notes accompany two classes given at the NRHEP2 school. In the first lecture I introduce the basic concepts used for analyzing well-posedness, that is the existence of a unique solution depending continuously on given data, of…
I will discuss, from a dynamical systems point of view, some recent attempts to rigorously derive the macroscopic laws of transport (e.g. the heat equation) from deterministic microscopic dynamics.
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Understanding design principles of complex cellular organization is one of the major challenges in biology. Recent analysis of the large-scale cellular organization has revealed the scale-free nature and robustness of metabolic and protein…
The interaction between natural selection and random mutation is frequently debated in recent years. Does similar dilemma also exist in the evolution of real networks such as biological networks? In this paper, we try to discuss this issue…
For decades, complex networks, such as social networks, biological networks, chemical networks, technological networks, have been used to study the evolution and dynamics of different kinds of complex systems. These complex systems can be…
This paper proposes a framework to ensure the existence of dynamical system trajectories in the state space of labeled, weighted, and attributed graphs. The evolution of such a system exhibits hybrid behavior: discrete jumps affecting the…
Understanding propagation mechanisms in complex networks is essential for fields like epidemiology and multi-robot networks. This paper reviews various propagation models, from traditional deterministic frameworks to advanced data-driven…
We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is…