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Traditional methods in educational research often fail to capture the complex and evolving nature of learning processes. This chapter examines the use of complex systems theory in education to address these limitations. The chapter covers…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization…
We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
Parabolic geometric flows have the property of smoothing for short time however, over long time, singularities are typically unavoidable, can be very nasty and may be impossible to classify. The idea of this paper is that, by bringing in…
Percolation has long served as a model for diverse phenomena and systems. The percolation transition, that is, the formation of a giant cluster on a macroscopic scale, is known as one of the most robust continuous transitions. Recently,…
The relaxation to equilibrium of lattice systems with long-range interactions is investigated. The timescales involved depend polynomially on the system size, potentially leading to diverging equilibration times. A kinetic equation for…
The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium of the…
What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow,…
Despite their importance in activated processes, transition-event durations -- which are much shorter than first passage times -- have not received a complete theoretical treatment. We therefore study the distribution of durations of…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
A. Gasull shared a list of 33 open problems in low dimensional dynamical systems in his work in 2021. The second part of Problem 3 is about whether the limit cycle of a quasi-homogeneous system $ \dot{x}=y,\; \dot{y}=-x^3+\alpha x^2y+y^3 $…
Over the past decade the study of fluidic droplets bouncing and skipping (or ``walking'') on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems,…
Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the…
This is a short survey on recent results obtained by the authors on dynamical phase transitions of interacting particle systems. We consider particle systems with exclusion dynamics, but it is conjectured that our results should hold for a…
Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the…
Since the publication of 'Complex Contagions and the Weakness of Long Ties' in 2007, complex contagions have been studied across an enormous variety of social domains. In reviewing this decade of research, we discuss recent advancements in…
External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical…
The most puzzling aspect of the glass transition observed in laboratory is an apparent decoupling of dynamics from structure. In this paper we recount the implication of various theories of glass transition for the static correlation length…