相关论文: A walk in the parameter space of L-H transitions w…

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…

Escape from a potential well through an index-1 saddle can be widely found in some important physical systems. Knowing the criteria and phase space geometry that govern escape events plays an important role in making use of such phenomenon,…

Bipedal balance is challenging due to its multi-phase, hybrid nature and high-dimensional state space. Traditional balance control approaches for bipedal robots rely on low-dimensional models for locomotion planning and reactive control,…

For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this…

We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area…

For piecewise-smooth ordinary differential equations, the occurrence of a Hopf bifurcation on a switching surface is known as a boundary Hopf bifurcation. Boundary Hopf bifurcations are codimension-two, so occur at points in two-parameter…

In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…

Varying one of the governing parameters of a dynamical system may lead to a critical transition, where the new stable state is undesirable. In some cases, there is only a limited range of the bifurcation parameter that corresponds to that…

We report a first study of time-dependent Probability Density Functions (PDFs) in the Low-to- High confinement mode (L-H) transition by extending the previous prey-predator-type model (Kim & Diamond, Phys. Rev. Lett. 91, 185006, 2003) to a…

We propose a new hybrid modelling approach that combines a mechanistic model with a machine-learnt model to predict the limit cycle oscillations of physical systems with a Hopf bifurcation. The mechanistic model is an ordinary differential…

We consider a paradigmatic nonvariational scalar Swift-Hohenberg equation that describes short wavenumber or large wavelength pattern forming systems. This work unveils evidence of the transition from stable stationary to moving localized…

We study the dynamics of spatially homogeneous Friedmann--Robertson--Walker universes filled with a massive scalar field in a neighbourhood of the massless transition $s=1$. At this point the Einstein--scalar system exhibits a…

We examine the effect of a slowly-varying time-dependent parameter on invasion fronts for which an unstable homogeneous equilibrium is invaded by either another homogeneous state or a spatially periodic state. We first explain and motivate…

We study the effect of changes in the parameters of a two-dimensional potential energy surface on the phase space structures relevant for chemical reaction dynamics. The changes in the potential energy are representative of chemical…

A standard motion control with feedback of the output displacement cannot handle unforeseen contact with environment without penetrating into the soft, i.e. viscoelastic, materials or even damaging the fragile materials. Robotics and…

The interplay between activity and elasticity often found in active and living systems triggers a plethora of autonomous behaviors ranging from self-assembly and collective motion to actuation. Amongst these, spontaneous self-oscillations…

We explore a two-body system with superexponential interactions that serves as a fundamental building block for a route to complexity. While being of striking simplicity this highly nonlinear interaction yields a plethora of intriguing…

Bifurcations leading to complex dynamical behaviour of non-linear systems are often encountered when the characteristics of feedback circuits in the system are varied. In systems with many unknown or varying parameters, it is an…

Within the framework of mode-coupling theory, the glass-transition scenario is investigated for a system of particles interacting with a hard-core repulsion and an additional square-shoulder soft core at larger distances. The static…

The appearance of topological effects in systems exhibiting a non-trivial topological band structure strongly relies on the coherent wave nature of the equations of motion. Here, we reveal topological dynamics in a classical stochastic…