A New Hyperchaotic Attractor with Complex Patterns
The paper introduces a new 4d dynamical system leading to a typical 4d strange attractor. Its focal statement appears in its total disconnection from previous 3D nonlinear systems.
nlin.CD↗
arXiv subjects
Safieddine Bouali
Publications and source records attributed to Safieddine Bouali.
A 3D Strange Attractor with a Distinctive Silhouette. The Butterfly Effect Revisited
We propose firstly an autonomous system of three first order differential equations which has two nonlinear terms and generating a new and distinctive strange attractor. Furthermore, this new 3D chaotic system performs a new feature of the Sensitive Dependency on Initial Conditions (SDIC) popularized as the Butterfly Effect discovered by Lorenz (1963). We noticed that the variation of the Initial Conditions for our system leads not only to different attractors but also to a singular phenomenon of overlapped attractors.
nlin.CD↗
A Novel Strange Attractor with a Stretched Loop
The paper introduces a new 3D strange attractor topologically different from any other known chaotic attractors. The intentionally constructed model of three autonomous first-order differential equations derives from the coupling-induced complexity of the well-known Lotka-Volterra oscillator. The chaotic attractor exhibiting a double scroll bridged by a loop mutates to a single scroll with a very stretched loop by the variation of one parameter. Analysis of the global behavior of the new low dimensional dissipative dynamical model and its range of periodic and a-periodic oscillations are presented.
nlin.CD↗
Twisting Rolls. An Heuristic Model and 3D Numerical Simulations of Vortex Patterns
We connect an appropriate feedback loop to a model of 2D vertical eddy of airflow which unfolds a wide range of vorticity behavior. Computational fluid dynamics of the twisted roll display a class of long lifespan 3D vortices. On the one hand, the infinitely stable columnar vortex simulated describes waterspouts and tornadoes with extended lifetime. On the other hand, a light modification of the retroaction exhibits strong similarities to tropical cyclones. Moreover, we investigate the outcome of the twisting process vertically shifted. This modelisation leads to the simulation of simultaneous vortices associated to this other class of 3D vortices with short lifespan. Our heuristic dynamical systems lay the foundations of a comprehensive modelisation of vortices since it joins theory and numerical simulations.
physics.flu-dyn↗
The Hunt Hypothesis and the Dividend Policy of the Firm. The Chaotic Motion of the Profits
We have carried out simulations of a financial model of the firm to analyse the validity of the concept of Trade on Equity in dynamics. The results exhibit the ability of the borrowing policy connected to a cautious dividend distribution to inject chaos into the profit motion. The 3D system built with the van der Pol's oscillator produces a new class of strange attractors.
nlin.CD↗