Julia Sets: Fractal Basin Boundaries

1992 ◽  
pp. 351-414
Author(s):  
Heinz-Otto Peitgen ◽  
Hartmut Jürgens ◽  
Dietmar Saupe
Keyword(s):  
Julia Sets ◽  
Fractal Basin Boundaries ◽  
Basin Boundaries

Julia Sets: Fractal Basin Boundaries

1992 ◽  
pp. 769-840
Author(s):  
Heinz-Otto Peitgen ◽  
Hartmut Jürgens ◽  
Dietmar Saupe
Keyword(s):  
Julia Sets ◽  
Fractal Basin Boundaries ◽  
Basin Boundaries

Julia Sets: Fractal Basin Boundaries

2004 ◽  
pp. 715-781
Author(s):  
Heinz-Otto Peitgen ◽  
Hartmut Jürgens ◽  
Dietmar Saupe
Keyword(s):  
Julia Sets ◽  
Fractal Basin Boundaries ◽  
Basin Boundaries

Truncated-fractal basin boundaries in forced pendulum systems

1988 ◽  
Vol 60 (8) ◽  
pp. 665-668 ◽  
Author(s):  
Matthew Varghese ◽  
James S. Thorp
Keyword(s):  
Fractal Basin Boundaries ◽  
Forced Pendulum ◽  
Basin Boundaries

Fractal Basin Boundaries, Long-Lived Chaotic Transients, And Unstable-Unstable Pair Bifurcation

1983 ◽  
Vol 51 (10) ◽  
pp. 942-942 ◽  
Author(s):  
Celso Grebogi ◽  
Edward Ott ◽  
James A. Yorke
Keyword(s):  
Fractal Basin Boundaries ◽  
Chaotic Transients ◽  
Basin Boundaries

Fractal basin boundaries in coupled map lattices

1994 ◽  
Vol 50 (5) ◽  
pp. 3470-3473 ◽  
Author(s):  
Ying-Cheng Lai ◽  
Raimind L. Winslow
Keyword(s):  
Coupled Map Lattices ◽  
Fractal Basin Boundaries ◽  
Basin Boundaries

THE EFFECT OF NONLINEAR DAMPING ON THE UNIVERSAL ESCAPE OSCILLATOR

1999 ◽  
Vol 09 (04) ◽  
pp. 735-744 ◽  
Author(s):  
MIGUEL A. F. SANJUÁN
Keyword(s):  
Energy Dissipation ◽  
Period Doubling ◽  
Nonlinear Damping ◽  
Basins Of Attraction ◽  
Period Doubling Bifurcation ◽  
Damping Coefficient ◽  
Nonlinear Dissipation ◽  
Fractal Basin Boundaries ◽  
Basin Boundaries

This paper analyzes the role of nonlinear dissipation on the universal escape oscillator. Nonlinear damping terms proportional to the power of the velocity are assumed and an investigation on its effects on the dynamics of the oscillator, such as the threshold of period-doubling bifurcation, fractal basin boundaries and how the basins of attraction are destroyed, is carried out. The results suggest that increasing the power of the nonlinear damping, has similar effects as of decreasing the damping coefficient for a linearly damped case, showing the very importance of the level or amount of energy dissipation.

Fractal Basin Boundaries and Chaotic Motions in Spring-Pendulum System

2003 ◽  
Author(s):  
Aria Alasty ◽  
Rasool Shabani
Keyword(s):  
Numerical Simulations ◽  
Multiple Scales ◽  
Basins Of Attraction ◽  
Chaotic Attractors ◽  
Global Behavior ◽  
Chaotic Motions ◽  
Pendulum System ◽  
Fractal Basin Boundaries ◽  
System Parameters ◽  
Basin Boundaries

This study investigates chaotic response in the spring-pendulum system. In this system beside of strange attractors, multiple regular attractors may coexist for some values of system parameters, where it is important to study the global behavior of the system using the basin boundaries of the attractors. Multiple scales method is used to distinguish the regions of stable and unstable attractors. In unstable regions, bifurcation diagram and poincare´ maps are used to study the existence of quasi-periodic and chaotic attractors. Results show that the jumping phenomena may occur when multiple regular attractors exist and for this case fractal basins of attraction are developed using numerical simulations.

scholarly journals Scaling properties of saddle-node bifurcations on fractal basin boundaries

2003 ◽  
Vol 68 (6) ◽  
Author(s):  
Romulus Breban ◽  
Helena E. Nusse ◽  
Edward Ott
Keyword(s):  
Fractal Basin Boundaries ◽  
Scaling Properties ◽  
Saddle Node ◽  
Basin Boundaries

Fractal basin boundaries

1985 ◽  
Vol 17 (2) ◽  
pp. 125-153 ◽  
Author(s):  
Steven W. McDonald ◽  
Celso Grebogi ◽  
Edward Ott ◽  
James A. Yorke
Keyword(s):  
Fractal Basin Boundaries ◽  
Basin Boundaries
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