The first portion of this paper contains an overview of recent progress in the development of dynamical-systems-based methods for the computation of Lagrangian transport processes in physical oceanography. We review the considerable progress made in...
Global dynamic results are obtained for families of competitive systems of difference equations of the form x n + 1 = b 1 x n α 1 + x n + c 1 y n , y n + 1 = b 2 y n α 2 + c 2 x n + y n n...
In this paper, we study the local, global, and bifurcation properties of a planar nonlinear asymmetric discrete model of Ricker type that is derived from a Darwinian evolution strategy based on evolutionary game theory. We make a change of variables...
Stable attitude control of unmanned or autonomous operations of vehicles moving in three spatial dimensions is essential for safe and reliable operations. Rigid body attitude control is inherently a nonlinear control problem, as the Lie group of rigi...
In this paper, we prove that the Taylor expansions of analytic functions appearing in the linearization of quadratic maps at hyperbolic fixed points do not successfully approximate invariant manifolds, such as stable and unstable manifolds, when high...
Eddy-driven jets are of importance in the ocean and atmosphere, and to a first approximation are governed by Rossby wave dynamics. This study addresses the time-dependent flux of fluid and a passive tracer between such a jet and an adjacent eddy, wit...
The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affi...
In this paper, we analyse the classical action as a tool to reveal the phase space structure of Hamiltonian systems simply and intuitively. We construct a scalar field using the values of the action along the trajectories to analyse the phase space....
Recently, Aydiner considered dark matter (DM) and dark energy (DE) as two open, non-equilibrium thermodynamic systems, which have heat changes and particle number changes but have no volume changes. These systems are described by nonlinear coupled eq...
We examine the modified Hill three-body problem by incorporating the oblateness of the primary body and focus on its asymptotic orbits. Specifically, we analyze and characterize homoclinic and heteroclinic connections associated with the collinear eq...
Ewing sarcoma is an aggressive pediatric cancer of enigmatic cellular origins typically resulting from a single translocation event t (11; 22) (q24; q12). The resulting fusion gene, EWSR1-FLI1, is toxic or unstable in most primary tissues. Consequent...
A marked interest has recently emerged regarding the analysis of the wall shear stress (WSS) vector field topological skeleton in cardiovascular flows. Based on dynamical system theory, the WSS topological skeleton is composed of fixed points, i.e.,...
A dynamic model is established to investigate the shimmy instability of a landing gear system, considering the influence of nonlinear damping. The stability criterion is utilized to determine the critical speed at which the landing gear system become...
The paper presents the development of a fully-safe, automatic rendezvous strategy between a passive vehicle and an active one orbiting around the Earth–Moon L2 Lagrangian point. This is one of the critical phases of future missions to permanently ret...
This paper deals with a diffusive predator–prey model with two delays. First, we consider the local bifurcation and global dynamical behavior of the kinetic system, which is a predator–prey model with cooperative hunting and Allee effect....