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Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…
Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…
We use a generalised version of the individual-based Tangled Nature model of evolutionary ecology to study the relationship between ecosystem structure and evolutionary history. Our evolved model ecosystems typically exhibit interaction…
The work presented in this thesis concerns different aspects of dynamical processes on networks. The first subject considered is the theoretical modeling of exploration processes of complex networks, such as the ``traceroute'' process used…
The microscopic bidomain problem with FitzHhugh-Nagumo ionic transport is studied in the $L_p\!-\!L_q$-framework. Reformulating the problem as a semilinear evolution equation on the interface, local well-posedness is proved in strong as…
This paper aims to the conditions of traffic flow evolving to stability and the stability of equilibrium under demand time-varying of traffic networks. The general framework of the evolution of flow dynamics by adopting evolutionary game…
In this paper we study hyperbolic and parabolic nonlinear partial differential equation models, which describe the evolution of two intersecting pedestrian flows. We assume that individuals avoid collisions by sidestepping, which is encoded…
We present a continuous-time link-based kinematic wave model (LKWM) for dynamic traffic networks based on the scalar conservation law model. Derivation of the LKWM involves the variational principle for the Hamilton-Jacobi equation and…
Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation…
Most existing works on transportation dynamics focus on networks of a fixed structure, but networks whose nodes are mobile have become widespread, such as cell-phone networks. We introduce a model to explore the basic physics of…
A novel Markovian network evolution model is introduced and analysed by means of information theory. It will be proved that the model, called Network Evolution Chain, is a stationary and ergodic stochastic process. Therefore, the Asymptotic…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
Real networks are complex dynamical systems, evolving over time with the addition and deletion of nodes and links. Currently, there exists no principled mathematical theory for their dynamics -- a grand-challenge open problem. Here, we show…
Networks are essential models in many applications such as information technology, chemistry, power systems, transportation, neuroscience, and social sciences. In light of such broad applicability, a general theory of dynamical systems on…
Highly-optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is non-convex and characterized by…
Besides the complexity in time or in number of messages, a common approach for analyzing distributed algorithms is to look at the assumptions they make on the underlying network. We investigate this question from the perspective of network…
We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case,…
Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation on a bounded domain, subject to a dynamic boundary condition. We also consider the limit parabolic problem with the same dynamic boundary…
Signal transduction networks can form highly interconnected systems within cells due to network crosstalk, the sharing of input signals between multiple downstream responses. To better understand the evolutionary design principles…