Dynamical behavior and Poincare section of fractional-order centrifugal governor system

2021 ◽  
Vol 182 ◽  
pp. 791-806
Author(s):  
J. Alidousti ◽  
Z. Eskandari
Keyword(s):  
Fractional Order ◽  
Dynamical Behavior ◽  
Poincaré Section ◽  
Poincare Section

scholarly journals Two-Parameter Dynamics of An Autonomous Mechanical Governor System With Time Delay

2021 ◽  
Author(s):  
Shuning Deng ◽  
Jinchen Ji ◽  
Guilin Wen ◽  
Huidong Xu
Keyword(s):  
Time Delay ◽  
Dynamical Behavior ◽  
Evolutionary Process ◽  
Basins Of Attraction ◽  
Poincaré Section ◽  
Poincare Section ◽  
Interesting Phenomenon ◽  
Computing Technique ◽  
Intersection Points ◽  
Two Parameter

Abstract Understanding of dynamical behavior in the parameter-state space plays a vital role in the optimal design and motion control of mechanical governor systems. By combining the GPU parallel computing technique with two determinate indicators, namely, the Lyapunov exponents and Poincaré section, this paper presents a detailed study on the two-parameter dynamics of a mechanical governor system with different time delays. By identifying different system responses in two-parameter plane, it is shown that the complexity of evolutionary process can increase significantly with the increase of time delay. The path-following strategy and the time domain collocation method are used to explore the details of the evolutionary process. An interesting phenomenon is found in the dynamical behavior of the delayed governor system, which can cause the inconsistency between the number of intersection points of certain periodic response on Poincaré section and the actual period characteristic. For example, the commonly exhibited period-1 orbit may have two or more intersection points on the Poincaré section instead of one point. Furthermore, the variations of basins of attraction are also discussed in the plane of initial history conditions to demonstrate the observed multistability phenomena and chaotic transitions.

scholarly journals Dynamical Monte Carlo Simulations of 3-D Galactic Systems in Axisymmetric and Triaxial Potentials

2017 ◽  
Vol 34 ◽  
Author(s):  
Ali Taani ◽  
Juan C. Vallejo
Keyword(s):  
Phase Space ◽  
Invariant Tori ◽  
Dynamical Behavior ◽  
Dark Halo ◽  
Short Axis ◽  
Poincaré Section ◽  
Invariant Curves ◽  
Poincare Section ◽  
Dynamical Behaviors ◽  
Stable Periodic

AbstractWe describe the dynamical behavior of isolated old ( ⩾ 1Gyr) objects-like Neutron Stars (NSs). These objects are evolved under smooth, time-independent, gravitational potentials, axisymmetric and with a triaxial dark halo. We analysed the geometry of the dynamics and applied the Poincaré section for comparing the influence of different birth velocities. The inspection of the maximal asymptotic Lyapunov (λ) exponent shows that dynamical behaviors of the selected orbits are nearly the same as the regular orbits with 2-DOF, both in axisymmetric and triaxial when (ϕ, qz)= (0,0). Conversely, a few chaotic trajectories are found with a rotated triaxial halo when (ϕ, qz)= (90, 1.5). The tube orbits preserve direction of their circulation around either the long or short axis as appeared in the triaxial potential, even when every initial condition leads to different orientations. The Poincaré section shows that there are 2-D invariant tori and invariant curves (islands) around stable periodic orbits that bound to the surface of 3-D tori. The regularity of several prototypical orbits offer the means to identify the phase-space regions with localized motions and to determine their environment in different models, because they can occupy significant parts of phase-space depending on the potential. This is of particular importance in Galactic Dynamics.

Adaptive Synchronization of Fractional-Order Coupled Neurons Under Electromagnetic Radiation

2020 ◽  
Vol 30 (03) ◽  
pp. 2050044
Author(s):  
Fanqi Meng ◽  
Xiaoqin Zeng ◽  
Zuolei Wang ◽  
Xinjun Wang
Keyword(s):  
Electromagnetic Radiation ◽  
Fractional Order ◽  
Dynamical Behavior ◽  
Lyapunov Stability Theory ◽  
Neuronal Model ◽  
Adaptive Synchronization ◽  
Dynamical Characteristics ◽  
Single Controller ◽  
Improved Model ◽  
Complex Dynamical Behavior

In this paper, we investigate the dynamical characteristics of four-variable fractional-order Hindmarsh–Rose neuronal model under electromagnetic radiation. The numerical results show that the improved model exhibits more complex dynamical behavior with more bifurcation parameters. Meanwhile, based on the fractional-order Lyapunov stability theory, we propose two adaptive control methods with a single controller to realize chaotic synchronization between two coupled neurons. Finally, numerical simulations show the feasibility and effectiveness of the presented method.

Dynamical Analysis and Circuit Simulation of a New Fractional-Order Hyperchaotic System and Its Discretization

2016 ◽  
Vol 26 (13) ◽  
pp. 1650222 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
A. Elsonbaty ◽  
A. A. Elsadany ◽  
A. E. Matouk
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Control Technique ◽  
Order System ◽  
Qualitative Behavior ◽  
Hyperchaotic System

This paper presents an analytical framework to investigate the dynamical behavior of a new fractional-order hyperchaotic circuit system. A sufficient condition for existence, uniqueness and continuous dependence on initial conditions of the solution of the proposed system is derived. The local stability of all the system’s equilibrium points are discussed using fractional Routh–Hurwitz test. Then the analytical conditions for the existence of a pitchfork bifurcation in this system with fractional-order parameter less than 1/3 are provided. Conditions for the existence of Hopf bifurcation in this system are also investigated. The dynamics of discretized form of our fractional-order hyperchaotic system are explored. Chaos control is also achieved in discretized system using delay feedback control technique. The numerical simulation are presented to confirm our theoretical analysis via phase portraits, bifurcation diagrams and Lyapunov exponents. A text encryption algorithm is presented based on the proposed fractional-order system. The results show that the new system exhibits a rich variety of dynamical behaviors such as limit cycles, chaos and transient phenomena where fractional-order derivative represents a key parameter in determining system qualitative behavior.

scholarly journals The onset of chaos in vortex sheet flow

2002 ◽  
Vol 454 ◽  
pp. 47-69 ◽  
Author(s):  
ROBERT KRASNY ◽  
MONIKA NITSCHE
Keyword(s):  
Vortex Ring ◽  
Vortex Core ◽  
Axisymmetric Flow ◽  
Period Doubling ◽  
Vortex Sheet ◽  
Small Scale ◽  
Poincaré Section ◽  
Poincare Section ◽  
Sheet Flow ◽  
Onset Of Chaos

Regularized point-vortex simulations are presented for vortex sheet motion in planar and axisymmetric flow. The sheet forms a vortex pair in the planar case and a vortex ring in the axisymmetric case. Initially the sheet rolls up into a smooth spiral, but irregular small-scale features develop later in time: gaps and folds appear in the spiral core and a thin wake is shed behind the vortex ring. These features are due to the onset of chaos in the vortex sheet flow. Numerical evidence and qualitative theoretical arguments are presented to support this conclusion. Past the initial transient the flow enters a quasi-steady state in which the vortex core undergoes a small-amplitude oscillation about a steady mean. The oscillation is a time-dependent variation in the elliptic deformation of the core vorticity contours; it is nearly time-periodic, but over long times it exhibits period-doubling and transitions between rotation and nutation. A spectral analysis is performed to determine the fundamental oscillation frequency and this is used to construct a Poincaré section of the vortex sheet flow. The resulting section displays the generic features of a chaotic Hamiltonian system, resonance bands and a heteroclinic tangle, and these features are well-correlated with the irregular features in the shape of the vortex sheet. The Poincaré section also has KAM curves bounding regions of integrable dynamics in which the sheet rolls up smoothly. The chaos seen here is induced by a self-sustained oscillation in the vortex core rather than external forcing. Several well-known vortex models are cited to justify and interpret the results.

Fractal-fractional order dynamical behavior of an HIV/AIDS epidemic mathematical model

2021 ◽  
Vol 136 (1) ◽  
Author(s):  
Zeeshan Ali ◽  
Faranak Rabiei ◽  
Kamal Shah ◽  
Touraj Khodadadi
Keyword(s):  
Mathematical Model ◽  
Fractional Order ◽  
Dynamical Behavior ◽  
Aids Epidemic ◽  
Hiv Aids

Chaotic Oscillator Based on Fractional Order Memcapacitor

2019 ◽  
Vol 28 (14) ◽  
pp. 1950239 ◽  
Author(s):  
Akif Akgul
Keyword(s):  
Mathematical Model ◽  
Lyapunov Exponents ◽  
Fractional Order ◽  
Nonlinear Oscillator ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Chaotic Oscillator ◽  
State Equations ◽  
Chaotic Oscillators ◽  
Eigen Values

Many literatures have discussed fractional order memristor and memcapacitor-based chaotic oscillators but the entire oscillator model is considered to be of fractional order. My interest is to propose a nonlinear oscillator with considering only the memcapacitor element of fractional order. Hence, I propose a fractional order memcapacitor (FMC)-based novel chaotic oscillator. The complete mathematical model for the proposed oscillator is derived and presented in this paper. The dimensionless state equations are then analyzed by using the equilibrium points and their stability, Eigen values, Kaplan–Yorke dimensions and Lyapunov exponents. To understand the complete dynamical behavior, bifurcation graphs are obtained and presented. Finally, the proposed fractional memcapacitor oscillator is implemented by using the shelf components.

scholarly journals Aspects of laser Lorenz dynamics

1994 ◽  
Vol 36 (2) ◽  
pp. 152-174 ◽  
Author(s):  
P. B. Chapman
Keyword(s):  
Hopf Bifurcation ◽  
Poincaré Section ◽  
Poincare Section ◽  
Lorenz Equations

AbstractThe laser Lorenz equations are studied by reducing them to a form suitable for application of an extension of a method developed by Kuzmak. The method generates a flow in a Poincaré section from which it is inferred that a certain Hopf bifurcation is always subcritical.

COMPUTER ASSISTED VERIFICATION OF CHAOS IN THE SMOOTH CHUA'S EQUATION

2008 ◽  
Vol 18 (08) ◽  
pp. 2391-2396 ◽  
Author(s):  
QUAN YUAN ◽  
XIAO-SONG YANG
Keyword(s):  
Poincaré Map ◽  
Chaotic Behavior ◽  
Computer Assisted ◽  
Poincaré Section ◽  
Poincare Map ◽  
Poincare Section ◽  
Numerical Studies ◽  
Topological Horseshoes

In this paper, chaos in the smooth Chua's equation is revisited. To confirm the chaotic behavior in the smooth Chua's equation demonstrated in numerical studies, we resort to Poincaré section and Poincaré map technique and present a computer assisted verification of existence of horseshoe chaos by virtue of topological horseshoes theory.

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