A new procedure for exploring chaotic attractors in nonlinear dynamical systems under random excitations

2011 ◽  
Vol 27 (4) ◽  
pp. 593-601 ◽  
Author(s):  
Chun-Biao Gan ◽  
Hua Lei
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical

Generating Fully Bounded Chaotic Attractors

2013 ◽  
pp. 148-153
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Properties ◽  
The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

Generating Fully Bounded Chaotic Attractors

2011 ◽  
Vol 2 (3) ◽  
pp. 36-42
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Properties ◽  
The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

scholarly journals Chaos and Complexity Dynamics of Evolutionary Systems

2020 ◽  
Author(s):  
Lal Mohan Saha
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Chaotic Motion ◽  
Correlation Dimension ◽  
Nonlinear Dynamical Systems ◽  
Chaotic Attractors ◽  
Tabular Form ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical

Chaotic phenomena and presence of complexity in various nonlinear dynamical systems extensively discussed in the context of recent researches. Discrete as well as continuous dynamical systems both considered here. Visualization of regularity and chaotic motion presented through bifurcation diagrams by varying a parameter of the system while keeping other parameters constant. In the processes, some perfect indicator of regularity and chaos discussed with appropriate examples. Measure of chaos in terms of Lyapunov exponents and that of complexity as increase in topological entropies discussed. The methodology to calculate these explained in details with exciting examples. Regular and chaotic attractors emerging during the study are drawn and analyzed. Correlation dimension, which provides the dimensionality of a chaotic attractor discussed in detail and calculated for different systems. Results obtained presented through graphics and in tabular form. Two techniques of chaos control, pulsive feedback control and asymptotic stability analysis, discussed and applied to control chaotic motion for certain cases. Finally, a brief discussion held for the concluded investigation.

Using Strange Attractors to Control Sound Processing in Live Electroacoustic Composition

2015 ◽  
Vol 39 (3) ◽  
pp. 25-45
Author(s):  
Miroslav Spasov
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Nonlinear Dynamical Systems ◽  
Chaotic Attractors ◽  
Live Electronics ◽  
Tenor Saxophone ◽  
Sound Processing ◽  
Nonlinear Dynamical ◽  
Interactive Composition ◽  
Mathematical Equations

This article explores the possibility of using chaotic attractors to control sound processing with software instruments in live electroacoustic composition. The practice-led investigation involves the Attractors Library, a collection of Max/MSP externals based on iterative mathematical equations representing nonlinear dynamical systems; Attractors Player, a Max/MSP patch that controls the attractors' performance and live processing; and the two compositions based on the software: Strange Attractions for flute, clarinet, horn, and live electronics, and Sabda Vidya No. 2 for flute, tenor saxophone, and live electronics. In the article I discuss some specific attractors' characteristics and their use in interactive composition, relying on the experience from the performances of these two compositions. The idea is to highlight the experience with these nonlinear systems and to encourage other composers to use them in their own works.

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