This review presents an overview of Lorenz models between 1960 and 2008, classified into
six categories based on different types of Partial Differential Equations (PDEs). These …

The 1960s was an exciting era for atmospheric predictability research: a finite predictability
of the atmosphere was uncovered using Lorenz's models and the well-acknowledged …

Definition To determine whether (or not) the intrinsic predictability limit of the atmosphere is
two weeks and whether (or not) Lorenz's approaches support this limit, this entry discusses …

Definition Within Lorenz models, the three major kinds of butterfly effects (BEs) are the
sensitive dependence on initial conditions (SDIC), the ability of a tiny perturbation to create …

To describe the time evolution of infected persons associated with an epidemic wave, we
recently derived the KdV-SIR equation that is mathematically identical to the Kortewegde …

The interaction between tropical clouds and radiation is studied in the context of the weak
temperature gradient approximation, using very low order systems (eg, a two-column two …

Lorenz rediscovered the butterfly effect, which is defined as the sensitive dependence on
initial conditions (SDIC), in 1963. In 1972, he used the term “butterfly” as a metaphor to …

Here we present the numerical methods, applications, and comparisons with observations
and previous studies. It includes numerical analyses of shallow water equations, Sun's …

Multistability is an important concept that refers to the coexistence of multiple solutions.
Although significant studies reported the emergence of multistability, a few studies have …

The role of chaos in the climate system has been dismissed as high dimensional turbulence
and noise, with minimal impact on long-term climate change. However theory and …