Physics NotePublished
Gap Road: A New Path to Chaos
M. C. S. Vieira; C. Tsallis
1988
Publication details
- Authors
- M. C. S. Vieira; C. Tsallis
- Type
- Physics Note
- Status
- Published
- Publication date
- 1988
- Description
- We study numerically the asymmetric map <math>x'=1-\varepsilon_i-a_i |x|^{z_i}</math> <math>( \,\!</math>i=1,2 respectively, correspond to <math>x>0\,\!</math> and <math>x\leqq 0)</math>. The standard logisticlike equation is recovered for <math>a_1=a_2\,\!</math>, <math>z_1=z_2=2\,\!</math> and <math>\varepsilon_1= \varepsilon_2=0</math>. Three types of asymmetry are studied, namely those concerning the amplitude <math>(a_1 \ne a_2) \,\!</math>, the exponent <math>(z_1 \ne z_2) \,\!</math> and a possible discontinuity <math>(\varepsilon_1 \ne \varepsilon_2) \,\!</math> the well known period -doubling road to chaos is topologically unmodified in the two first cases, but in the last one the scenario is completely new ("gap road to chaos"). Chaos is now attained through sequences of inverse cascades. Various new features are observed concerning the phase-diagrams, Liapunov and uncertainty exponent, number of attractors, multifractality, among others.
- Year
- 1988
- Number
- CBPF-NF-025/88
- Linked to a thesis
- No
- Linked to a grant
- No