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.

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.

A New Method for Equilibria and Stability Analysis of Nonlinear Dynamical Systems

2014 ◽  
Vol 534 ◽  
pp. 131-136
Author(s):  
Long Cao ◽  
Yi Hua Cao
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Numerical Continuation ◽  
Vehicle Model ◽  
Nonlinear Dynamical ◽  
Novel Method ◽  
Linearized System ◽  
Continuation Algorithm

A novel method based on numerical continuation algorithm for equilibria and stability analysis of nonlinear dynamical system is introduced and applied to an aircraft vehicle model. Dynamical systems are usually modeled with differential equations, while their equilibria and stability analysis are pure algebraic problems. The newly-proposed method in this paper provides a way to solve the equilibrium equation and the eigenvalues of the locally linearized system simultaneously, which avoids QR iterations and can save much time.

scholarly journals State Observation for Lipschitz Nonlinear Dynamical Systems Based on Lyapunov Functions and Functionals

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1424 ◽  
Author(s):  
Angelo Alessandri ◽  
Patrizia Bagnerini ◽  
Roberto Cianci
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Lyapunov Functions ◽  
Nonlinear Dynamical Systems ◽  
Estimation Error ◽  
Stability Conditions ◽  
Nonlinear Dynamical ◽  
State Observation ◽  
State Observers ◽  
The Stability

State observers for systems having Lipschitz nonlinearities are considered for what concerns the stability of the estimation error by means of a decomposition of the dynamics of the error into the cascade of two systems. First, conditions are established in order to guarantee the asymptotic stability of the estimation error in a noise-free setting. Second, under the effect of system and measurement disturbances regarded as unknown inputs affecting the dynamics of the error, the proposed observers provide an estimation error that is input-to-state stable with respect to these disturbances. Lyapunov functions and functionals are adopted to prove such results. Third, simulations are shown to confirm the theoretical achievements and the effectiveness of the stability conditions we have established.

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 Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Min Wu ◽  
Zhengfeng Yang ◽  
Wang Lin
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Lyapunov Functions ◽  
Nonlinear Dynamical Systems ◽  
Region Of Attraction ◽  
Nonlinear Dynamical ◽  
Recovery Techniques ◽  
Regions Of Attraction

We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.

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