Transitions are to be found throughout the natural world. The laws of nature are usually
represented by differential equations, which can be regarded as dynamical systems—both …

A general, variational approach to derive low-order reduced models from possibly non-
autonomous systems is presented. The approach is based on the concept of optimal …

We study the stability and dynamic transitions of a diffusive predator–prey model with Allee
effect on prey in a two-dimensional domain. Our tool includes the recently developed …

Our Earth's atmosphere and oceans are rotating geophysical fluids that are two important
components of the planet's climate system. The atmosphere and the oceans are extremely …

We study the stability and dynamic transition of a rotating electrically conducting fluid layer in
the presence of an external magnetic field based on the Boussinesq approximation. By …

In this paper, we aim to investigate the dynamic transition of the Klausmeier-Gray-Scott
(KGS) model in a rectangular domain or a square domain. Our research tool is the dynamic …

In this article, we aim to classify the dynamic transitions and bifurcations for a family of
axisymmetric geophysical fluid problems of a generic fourth-second order structure. A …

Dynamic phase transitions of the Brusselator model is carefully analyzed, leading to a
rigorous characterization of the types and structure of the phase transitions of the model from …

The current article focuses on the examination of nonlinear instability and dynamic
transitions in a double-diffusive rotating couple-stress fluid layer. The analysis was based on …

The main objective of this article is to study the dynamic phase transitions associated with
the spatial–temporal oscillations of the BZ reactions, given by Field, Körös and Noyes, also …