Related papers: Forward and Pullback Dynamics of Nonautonomous Int…

Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…

This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new…

Long-range dependence and non-Gaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. However, it is not always appreciated that both phenomena may occur together in natural systems and that…

We introduce a method for learning the dynamics of complex nonlinear systems based on deep generative models over temporal segments of states and actions. Unlike dynamics models that operate over individual discrete timesteps, we learn the…

We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…

Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. However, building accurate long-term prediction models remains challenging due to the limitations of existing temporal…

General-purpose trajectory planning algorithms for automated driving utilize complex reward functions to perform a combined optimization of strategic, behavioral, and kinematic features. The specification and tuning of a single reward…

We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse…

We study the evolutionary dynamics of games under environmental feedback using replicator equations for two interacting populations. One key feature is to consider jointly the co-evolution of the dynamic payoff matrices and the state of the…

Indirect reciprocity maintains cooperation in stranger societies by mapping individual behaviors onto reputation signals via social norms. Existing theoretical frameworks assume static environments with constant resources and fixed payoff…

We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…

This paper presents a general theory that aims at explaining timescales observed empirically in technology transitions and predicting those of future transitions. This framework is used further to derive a theory for exploring the dynamics…

A parametric family of reaction-diffusion equations with nonlocal viscosity is considered. Existence of solutions and actually of pullback attractors is known from previous works. In this paper we obtain a robustness result of the…

Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…

We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…

Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an…

Homophily and social influence are the fundamental mechanisms that drive the evolution of attitudes, beliefs and behaviour within social groups. Homophily relates the similarity between pairs of individuals' attitudinal states to their…

A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…

This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…