Related papers: Rate-induced tipping in complex high-dimensional e…

Current early warning signs for tipping points often fail to distinguish between catastrophic shifts and less dramatic state changes, such as spatial pattern formation. This paper introduces a novel method that addresses this limitation by…

When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…

There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations. In particular, the term `tipping', or critical transition has in recent years entered…

We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise…

We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of…

The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…

Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general…

Eco-evolutionary dynamics, or eco-evolution for short, are thought to involve rapid demography (ecology) and equally rapid phenotypic changes (evolution) leading to novel, emergent system behaviours. This focus on contemporary dynamics is…

A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…

In a constantly changing world, animals must account for environmental volatility when making decisions. To appropriately discount older, irrelevant information, they need to learn the rate at which the environment changes. We develop an…

Tipping points characterize situations where a regulated system may experience a sudden and irreversible change and are generally associated with a random state of the system below which the change materializes. In this paper, we study a…

Plankton blooms are complex nonlinear phenomena whose occurrence can be described by the two-timescale (fast-slow) phytoplankton-zooplankton model intrpduced by Truscott and Brindley 1994. In their work, they observed that a sufficiently…

One way to warn of forthcoming critical transitions in Earth system components is using observations to detect declining system stability. It has also been suggested to extrapolate such stability changes into the future and predict tipping…

Learning in artificial neural networks usually relies on continuous, externally driven weight updates, in which parameters are modified at every step in response to incoming data, error signals or reward feedback. In this setting, routine…

Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…

We have analyzed phenology data and protein configurations from molecular dynamics simulations with the nonlinear forecasting method proposed by May and Sugihara. Our primary focus in this work is to characterize the dynamic state of a…

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…

A function with finite asymptotic limits gives rise to a transition equation between a "past system" and a "future system". This question is analyzed in the case of nonautonomous coercive nonlinear scalar ordinary differential equations…

Collapses of dynamical systems into irrecoverable states are observed in ecosystems, human societies, financial systems and network infrastructures. Despite their widespread occurrence and impact, these events remain largely unpredictable.…

Time-varying parameters (TVPs) models are frequently used in economics to capture structural change. I highlight a rather underutilized fact -- that these are actually ridge regressions. Instantly, this makes computations, tuning, and…