Multiple attractors and strange nonchaotic dynamical behavior in a periodically forced system

2021 ◽  
Vol 105 (4) ◽  
pp. 3615-3635
Author(s):  
A. Chithra ◽  
I. Raja Mohamed
Keyword(s):  
Dynamical Behavior ◽  
Multiple Attractors

scholarly journals Experimental Validation of Multiple Attractors in a Simple Chaotic Circuit

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Theoretical Prediction ◽  
Chaotic System ◽  
Experimental Validation ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Experimental Results ◽  
Equilibrium Analysis ◽  
Tuning Parameter ◽  
Multiple Attractors

In this paper, a simple jerk circuit that allows studying the dynamical behavior of a three-dimensional autonomous chaotic system with only one nonlinear term is further investigated by numerical simulations and experimental validation. Depending on a single tuning parameter, the chaotic system is theoretically studied using standard techniques such as equilibrium analysis, bifurcation diagram, and Lyapunov exponents. Subsequently, the circuit that models the chaotic system is implemented to validate theoretical prediction experimentally. Despite the simple structure of the jerk circuit, experimental study of Fourier spectra has shown that the jerk circuit displays complex dynamics characterized by periodic limit cycles and aperiodic strange attractors. In addition, the jerk circuit has exhibited a wide tuning range and experimental results have shown good agreement with theoretical prediction except for few cases where numerical simulation has failed to accurately match experimental results due to sensitivity to initial conditions which is a signature of chaotic nonlinear systems.

THE INVERSE OPTIMAL CONTROL OF A CHAOTIC SYSTEM WITH MULTIPLE ATTRACTORS

2007 ◽  
Vol 21 (29) ◽  
pp. 1999-2007 ◽  
Author(s):  
XINGYUAN WANG ◽  
YONG GAO
Keyword(s):  
Optimal Control ◽  
Chaotic System ◽  
Control Method ◽  
Dynamical Behavior ◽  
Lyapunov Stability Theory ◽  
Inverse Optimal Control ◽  
Multiple Attractors ◽  
Unified Chaotic System ◽  
Optimal Control Method ◽  
Linear State

This paper studies the dynamical behavior of the Newton–Leipnik system and its trajectory-transformation control problem to multiple attractors. A simple linear state feedback controller for the Newton–Leipnik system based on the Lyapunov stability theory and applying the inverse optimal control method is designed. We stabilize asymptotically the chaotic attractors to unstable equilibriums of the system, so that the transformation of one attractor to another for the trajectory of the Newton–Leipnik system is realized. Theoretical analyses and numerical simulations both indicate the effectiveness of the controller. At last, the inverse optimal control method is proven effective for the chaotic systems with multiple attractors by the example on the unified chaotic system.

scholarly journals Dynamical Behavior of a 3D Jerk System with a Generalized Memristive Device

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Wei Feng ◽  
Yi-Gang He ◽  
Chun-Lai Li ◽  
Xun-Min Su ◽  
Xiao-Qing Chen
Keyword(s):  
Secure Communication ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Multiple Attractors ◽  
Memristive Device ◽  
Dynamical Behaviors ◽  
Coexistence Of Multiple Attractors ◽  
New Type ◽  
Hardware Circuit ◽  
Jerk System

As a new type of electronic components, a memristive device is receiving worldwide attention and can enrich the dynamical behaviors of the oscillating system. In this paper, we propose a 3D jerk system by introducing a generalized memristive device. It is found that the dynamical behaviors of the system are sensitive to the initial conditions even the system parameters are fixed, which results in the coexistence of multiple attractors. And there exists different transition behaviors depending on the selection of the parameters and initial values. Thereby, it is one important type of the candidate system for secure communication since the reconstruction of accurate state space becomes more difficult. Moreover, we build a hardware circuit and the experimental results effectively confirm the theoretical analyses.

Dynamical behavior of a nonlinear rotorcraft model

1989 ◽  
Author(s):  
GEORGE FLOWERS ◽  
BENSONH. TONGUE
Keyword(s):  
Dynamical Behavior

Probing the dynamical behavior in glass transition of PVPh-PEO blend

2021 ◽  
Vol 554 ◽  
pp. 120561
Author(s):  
Yong-jin Peng ◽  
He-Huang ◽  
Chang-jun Wang ◽  
Zhong-fu Zuo ◽  
Xue-zheng Liu
Keyword(s):  
Glass Transition ◽  
Dynamical Behavior

scholarly journals A Characterization of the Dynamics of Schröder’s Method for Polynomials with Two Roots

2021 ◽  
Vol 5 (1) ◽  
pp. 25
Author(s):  
Víctor Galilea ◽  
José M. Gutiérrez
Keyword(s):  
Nonlinear Equations ◽  
Complex Plane ◽  
Iterative Process ◽  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Schröder’S Method

The purpose of this work is to give a first approach to the dynamical behavior of Schröder’s method, a well-known iterative process for solving nonlinear equations. In this context, we consider equations defined in the complex plane. By using topological conjugations, we characterize the basins of attraction of Schröder’s method applied to polynomials with two roots and different multiplicities. Actually, we show that these basins are half-planes or circles, depending on the multiplicities of the roots. We conclude our study with a graphical gallery that allow us to compare the basins of attraction of Newton’s and Schröder’s method applied to some given polynomials.

scholarly journals Dynamics & Spectroscopy with Neutrons—Recent Developments & Emerging Opportunities

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1440
Author(s):  
Kacper Drużbicki ◽  
Mattia Gaboardi ◽  
Felix Fernandez-Alonso
Keyword(s):  
Dynamical Behavior ◽  
Disordered Materials ◽  
Spectroscopic Techniques ◽  
Computational Tools ◽  
Soft Solids ◽  
Sustainable Technologies ◽  
Energy Transfers ◽  
Recent Developments ◽  
Scientific Questions ◽  
Nuclear Quantum Effects

This work provides an up-to-date overview of recent developments in neutron spectroscopic techniques and associated computational tools to interrogate the structural properties and dynamical behavior of complex and disordered materials, with a focus on those of a soft and polymeric nature. These have and continue to pave the way for new scientific opportunities simply thought unthinkable not so long ago, and have particularly benefited from advances in high-resolution, broadband techniques spanning energy transfers from the meV to the eV. Topical areas include the identification and robust assignment of low-energy modes underpinning functionality in soft solids and supramolecular frameworks, or the quantification in the laboratory of hitherto unexplored nuclear quantum effects dictating thermodynamic properties. In addition to novel classes of materials, we also discuss recent discoveries around water and its phase diagram, which continue to surprise us. All throughout, emphasis is placed on linking these ongoing and exciting experimental and computational developments to specific scientific questions in the context of the discovery of new materials for sustainable technologies.

scholarly journals Dynamical analysis of a stochastic rumor-spreading model with Holling II functional response function and time delay

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liang’an Huo ◽  
Xiaomin Chen
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Functional Response ◽  
Response Function ◽  
Rapid Development ◽  
Dynamical Behavior ◽  
Deterministic System ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Holling Ii Functional Response

AbstractWith the rapid development of information society, rumor plays an increasingly crucial part in social communication, and its spreading has a significant impact on human life. In this paper, a stochastic rumor-spreading model with Holling II functional response function considering the existence of time delay and the disturbance of white noise is proposed. Firstly, the existence of a unique global positive solution of the model is studied. Then the asymptotic behavior of the global solution around the rumor-free and rumor-local equilibrium nodes of the deterministic system is discussed. Finally, through some numerical results, the validity and availability of theoretical analysis is verified powerfully, and it shows that some factors such as the transmission rate, the intensity of white noise, and the time delay have significant relationship with the dynamical behavior of rumor spreading.

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