Wada basin boundaries and generalized basin cells in a smooth and discontinuous oscillator

Author(s):  
Yongxiang Zhang
Keyword(s):  
1988 ◽  
Vol 60 (8) ◽  
pp. 665-668 ◽  
Author(s):  
Matthew Varghese ◽  
James S. Thorp

1992 ◽  
pp. 351-414
Author(s):  
Heinz-Otto Peitgen ◽  
Hartmut Jürgens ◽  
Dietmar Saupe

Author(s):  
T. Gökgöz ◽  
Y. Yayla ◽  
M. B. Yaman ◽  
H. Güvenç ◽  
S. Kaya

Although water use has been increasing day by day depending on fast population increase, urbanization and industrialization in the world, potential of usable water resources remains stable. On the other side, expansion of agricultural activities, industrialization, urbanization, global warming and climate change create a big pressure on current water resources. Therefore, management of water resources is one of the most significant problems of today that is required to be solved and ‘’Integrated Basin Management’’ has gained importance in the world in terms of decreasing environmental problems by more efficiently using current water resources. In order to achieve integrated basin management, it is needed to determine basin boundaries with sufficient accuracy and precision and encode them systematically. In various analyses to be done on the basis of basin, topographic parameters are also needed such as shape factor, bifurcation ratio, drainage frequency, drainage density, length of the main flow path, harmonic slope, average slope, time of concentration, hypsometric curve and maximum elevation difference. Nowadays, basin boundaries are obtained with digital elevation models in geographical information systems. However, tools developed for topographic parameters are not available. In this study, programs were written in Python programming language for afore-mentioned topographic parameters and each turned into a geographical information system tool. Therefore, a significant contribution has been made to the subject by completing the deficiency in the geographical information system devoted to the topographic parameters that are needed in almost every analyses concerning to the hydrology.


2015 ◽  
Vol 25 (02) ◽  
pp. 1550024 ◽  
Author(s):  
C. H. Miwadinou ◽  
A. V. Monwanou ◽  
J. B. Chabi Orou

This paper considers the effect of nonlinear dissipation on the basin boundaries of a driven two-well modified Rayleigh–Duffing oscillator where pure cubic, unpure cubic, pure quadratic and unpure quadratic nonlinearities are considered. By analyzing the potential, an analytic expression is found for the homoclinic orbit. The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos. Unpure quadratic parameter and parametric excitation amplitude effects are found on the critical Melnikov amplitude μ cr . Finally, the phase space of initial conditions is carefully examined in order to analyze the effect of the nonlinear damping, and particularly how the basin boundaries become fractalized.


1994 ◽  
Vol 50 (5) ◽  
pp. 3470-3473 ◽  
Author(s):  
Ying-Cheng Lai ◽  
Raimind L. Winslow

2021 ◽  
Vol 153 ◽  
pp. 111532
Author(s):  
André Gusso ◽  
Leandro E. de Mello

2013 ◽  
Vol 377 (18) ◽  
pp. 1274-1281 ◽  
Author(s):  
Yongxiang Zhang ◽  
Guanwei Luo

1999 ◽  
Vol 09 (04) ◽  
pp. 735-744 ◽  
Author(s):  
MIGUEL A. F. SANJUÁN

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.


Sign in / Sign up

Export Citation Format

Share Document