THE DOUBLE-CUSP MAP FOR THE FORCED LORENZ SYSTEM-Reference-Cited by-同舟云学术

THE DOUBLE-CUSP MAP FOR THE FORCED LORENZ SYSTEM

Published:2003-10 Issue:10 Volume:13 Page:3029-3035
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

MEHTA MITAXI¹,MITTAL A. K.¹²,DWIVEDI S.²

Affiliation:

1. Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019, India

2. Institute of Interdisciplinary Studies, M. N. Saha Centre of Space Studies, Department of Physics, Allahabad University, Allahabad 211002, India

Abstract

It is found that adding constant forcing terms to the Lorenz equations breaks the (x,y)→(-x,-y) symmetry of the system. As a result of the symmetry breaking the consecutive z max return map (the cusp map) gets split into a double-cusp map. We investigate the double-cusp map for the forced Lorenz system using approximate invariant manifolds about the fixed points and use the double-cusp map to understand the stability of the attractor.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127403008429

Reference8 articles.

1. Probability density of the Lorenz model

2. Analytic approximation of the Lorenz attractor by invariant manifolds

3. The exact invariant density for a cusp-shaped return map

4. Deterministic Nonperiodic Flow

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