Description and analysis of the time–domain response of nabla discrete fractional order systems

2020 ◽  
Author(s):  
Yiheng Wei ◽  
Qing Gao ◽  
Songsong Cheng ◽  
Yong Wang
Keyword(s):  
Fractional Order ◽  
Time Domain ◽  
Fractional Order Systems ◽  
Time Domain Response ◽  
The Time Domain

Improving the time domain response of fractional order digital differentiators by windowing

2015 ◽  
Vol 107 ◽  
pp. 282-289 ◽  
Author(s):  
Chengyan Peng ◽  
Xiaochuan Ma ◽  
Geping Lin ◽  
Min Wang
Keyword(s):  
Fractional Order ◽  
Time Domain ◽  
Time Domain Response ◽  
The Time Domain

A Note on the Lyapunov Stability of Fractional-Order Nonlinear Systems

2017 ◽  
Author(s):  
Sara Dadras ◽  
Soodeh Dadras ◽  
Hadi Malek ◽  
YangQuan Chen
Keyword(s):  
Exponential Stability ◽  
Fractional Order ◽  
Lyapunov Stability ◽  
Time Domain ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Sufficient Condition ◽  
Fractional Order Systems ◽  
The Stability ◽  
The Time Domain

In this paper, stability of fractional order (FO) systems is investigated in the sense of the Lyapunov stability theory. A new definition for exponential stability of the fractional order systems is given and sufficient conditions are obtained for the exponential stability of the FO systems using the notion of Lyapunov stability. Besides, a less conservative sufficient condition is derived for asymptotical stability of FO systems. The stability analysis is done in the time domain. Numerical examples are given to show that the obtained conditions are effective and applicable in practice.

Hybrid Projective Synchronization for the Fractional-Order Chen-Lee System and its Circuit Realization

2013 ◽  
Vol 300-301 ◽  
pp. 1573-1578
Author(s):  
Seng Kin Lao ◽  
Hsien Keng Chen ◽  
Lap Mou Tam ◽  
Long Jye Sheu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Body Motion ◽  
Projective Synchronization ◽  
Fractional Order Systems ◽  
Control Of Chaos ◽  
Circuit Realization ◽  
Hybrid Projective Synchronization ◽  
The Time Domain ◽  
Theoretical Analyses

The growing interest shows the importance of the control of chaos in fractional-order systems in recent years. This paper investigates in the hybrid projective synchronization of two chaotic systems with fractional-order, which were derived from Euler equations of rigid body motion. Theoretical analyses of the proposed methods are validated by numerical simulation in the time domain. Moreover, the synchronization system is realized using electronic circuits with fractance in the frequency domain.

BIFURCATIONS AND CHAOS IN FRACTIONAL-ORDER SIMPLIFIED LORENZ SYSTEM

2010 ◽  
Vol 20 (04) ◽  
pp. 1209-1219 ◽  
Author(s):  
KEHUI SUN ◽  
XIA WANG ◽  
J. C. SPROTT
Keyword(s):  
Fractional Order ◽  
Lorenz System ◽  
Complex Dynamics ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Fractional Order Systems ◽  
Wide Range ◽  
The Time Domain ◽  
Fractional Orders ◽  
Simplified Lorenz System

The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper, we numerically study the bifurcations and chaotic behaviors in the fractional-order simplified Lorenz system using the time-domain scheme. Chaos does exist in this system for a wide range of fractional orders, both less than and greater than three. Complex dynamics with interesting characteristics are presented by means of phase portraits, bifurcation diagrams and the largest Lyapunov exponent. Both the system parameter and the fractional order can be taken as bifurcation parameters, and the range of existing chaos is different for different parameters. The lowest order we found for this system to yield chaos is 2.62.

scholarly journals Scattering of an Impact Wave by a Crack in a Composite Plate

1992 ◽  
Vol 59 (3) ◽  
pp. 596-603 ◽  
Author(s):  
S. K. Datta ◽  
T. H. Ju ◽  
A. H. Shah
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Impact Load ◽  
Near Field ◽  
Boundary Integral ◽  
Transition Elements ◽  
Element Discretization ◽  
Crack Tips ◽  
Time Domain Response ◽  
The Time Domain

The surface responses due to impact load on an infinite uniaxial graphite/epoxy plate containing a horizontal crack is investigated both in time and frequency domain by using a hybrid method combining the finite element discretization of the near-field with boundary integral representation of the field outside a contour completely enclosing the crack. This combined method leads to a set of linear unsymmetric complex matrix equations, which are solved to obtain the response in the frequency domain by biconjugate gradient method. The time-domain response is then obtained by using an FFT. In order to capture the time-domain characteristics accurately, high-order finite elements have been used. Also, both the six-node singular elements and eight-node transition elements are used around the crack tips to model the crack-tip singularity. From the numerical results for surface responses it seems possible to clearly identify both the depth and length of this crack.

Improved analysis of the time domain response of scanning force microscope cantilevers

2000 ◽  
Vol 88 (12) ◽  
pp. 7321-7327 ◽  
Author(s):  
Brian A. Todd ◽  
Steven J. Eppell ◽  
Fredy R. Zypman
Keyword(s):  
Time Domain ◽  
Scanning Force Microscope ◽  
Scanning Force ◽  
Time Domain Response ◽  
The Time Domain
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