A ROUTE TO CHAOS IN ELECTROMECHANICAL SYSTEMS: PHASE SPACE ATTRACTION BASIN SWITCHING

Certain systems present chaotic dynamics when subjected to a regular periodic input. In a study of a nonlinear model of an electromechanical transducer, its dynamic stability is analyzed and it is observed to present chaotic dynamics when a squared signal is introduced as input to the excitor circuit voltage. It is demonstrated that the chaotic movement is due to the periodic modification in the attraction basin of the state space, caused by the input varying in time. Varying the input causes the system to cross saddle type bifurcation values in which points of equilibrium appear and disappear, periodically modifying the qualitative aspects of the system's phase space. This paper describes the deterministic chaos generation by the regular and periodic modification of the properties of the phase space.

Download Full-text

On periodically time-varying two-dimensional state-space filters

Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94 ◽

10.1109/iscas.1994.408944 ◽

2002 ◽

Cited By ~ 14

Author(s):

D.C. McLernon

Keyword(s):

State Space ◽

Time Varying ◽

Two Dimensional ◽

Dimensional State Space

Download Full-text

Combining a neural network with deterministic chaos theory using phase space reconstruction for daily rainfall-runoff forecasting

2015 12th International Symposium on Programming and Systems (ISPS) ◽

10.1109/isps.2015.7244983 ◽

2015 ◽

Author(s):

Mohamed Chettih ◽

Khaled Chorfi ◽

Kaddour Mouattah

Keyword(s):

Neural Network ◽

Phase Space ◽

Chaos Theory ◽

Deterministic Chaos ◽

Daily Rainfall ◽

Phase Space Reconstruction ◽

Rainfall Runoff ◽

Runoff Forecasting

Download Full-text

DETERMINISTIC CHAOS IN AN INTERPHASE LAYER OF A LIQUID–VAPOR SYSTEM

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127404011557 ◽

2004 ◽

Vol 14 (10) ◽

pp. 3671-3678

Author(s):

G. P. BYSTRAI ◽

S. I. IVANOVA ◽

S. I. STUDENOK

Keyword(s):

Phase Transitions ◽

Chaotic Dynamics ◽

Deterministic Chaos ◽

Second Order ◽

Homogeneous Layer ◽

Time Interval ◽

Evaporation And Condensation ◽

Starting Conditions ◽

Kolmogorov's Entropy ◽

Dimensional Mapping

A second-order nonlinear differential equation with an aftereffect for the density of a thin homogeneous layer on a liquid and vapor interface is considered. The acts of evaporation and condensation of molecules, which are regarded as periodic "impacts", excite the layer. The mentioned NDE is integrated over a finite time interval to find a 2D (two-dimensional) mapping whose numerical solution describes the chaotic dynamics of density and pressure in time. The algorithms of constructing bifurcation diagrams, Lyapunov's exponents and Kolmogorov's entropy for systems with first-order, second-order phase transitions and Van der Waals' systems were elaborated. This approach allows to associate such concepts as phase transition, deterministic chaos and nonlinear processes. It also allows to answer a question whether deterministic chaos occurs in systems with phase transitions and how fast the information about starting conditions is lost within them.

Download Full-text

Chaos in the Periodically Parametrically Excited Lorenz System

International Journal of Bifurcation and Chaos ◽

10.1142/s021812742130024x ◽

2021 ◽

Vol 31 (08) ◽

pp. 2130024

Author(s):

Weisheng Huang ◽

Xiao-Song Yang

Keyword(s):

Chaotic Dynamics ◽

Lorenz System ◽

Stable Equilibrium ◽

Chaotic Behavior ◽

Equilibrium Points ◽

Time Varying ◽

Asymptotically Stable ◽

Parametrically Excited ◽

The Lorenz System

We demonstrate in this paper a new chaotic behavior in the Lorenz system with periodically excited parameters. We focus on the parameters with which the Lorenz system has only two asymptotically stable equilibrium points, a saddle and no chaotic dynamics. A new mechanism of generating chaos in the periodically excited Lorenz system is demonstrated by showing that some trajectories can visit different attractor basins due to the periodic variations of the attractor basins of the time-varying stable equilibrium points when a parameter of the Lorenz system is varying periodically.

Download Full-text