This paper presents a novel 4D hyperchaotic system derived from a modified 3D Lorenz
chaotic system. A key aspect of this system is the presence of a single equilibrium point, and …

Persistence of solitary wave solutions of the regularized long wave equation with small
perturbations are investigated by the geometric singular perturbation theory and bifurcation …

One approach for describing spatiotemporal chaos is to study the unstable invariant sets
embedded in the chaotic attractor of the system. While equilibria, periodic orbits, and …

This work is a unified study of stable and unstable steady states of 2D active nematic
channel flow using the framework of Exact Coherent Structures (ECSs). ECSs are stationary …

Unstable periodic orbits (UPOs) are believed to be the underlying dynamical structures of
spatio-temporal chaos and turbulence. Finding these UPOs is however notoriously difficult …

Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the
behavior of a dynamical system can closely resemble that of a solution which is no longer …

Invariant solutions of the Navier–Stokes equations play an important role in the
spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these …

In this study, we perform an extensive numerical study of the one-dimensional Kuramoto-
Sivashinsky equation under time-periodic forces. We examine the statistics of chaotic …

One approach for describing spatio-temporally chaotic dynamical systems, including fluid
turbulence, is to study non-chaotic but unstable invariant solutions embedded within the …