Singular functions of a nonlinear pendulum on finite time intervals

2004 ◽  
Author(s):  
L.A. Mironovsky ◽  
X.Y. Petrova
Keyword(s):  
Finite Time ◽  
Time Intervals ◽  
Singular Functions ◽  
Nonlinear Pendulum

scholarly journals Caputo Fractional Differential Equations with Non-Instantaneous Random Erlang Distributed Impulses

2019 ◽  
Vol 3 (2) ◽  
pp. 28 ◽  
Author(s):  
Snezhana Hristova ◽  
Krasimira Ivanova
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Finite Time ◽  
Lyapunov Functions ◽  
Random Variable ◽  
Time Intervals ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Dini Derivatives ◽  
Moment Exponential Stability

The p-moment exponential stability of non-instantaneous impulsive Caputo fractional differential equations is studied. The impulses occur at random moments and their action continues on finite time intervals with initially given lengths. The time between two consecutive moments of impulses is the Erlang distributed random variable. The study is based on Lyapunov functions. The fractional Dini derivatives are applied.

scholarly journals A simple metric to quantify seismicity clustering

2010 ◽  
Vol 17 (4) ◽  
pp. 293-302 ◽  
Author(s):  
N. F. Cho ◽  
K. F. Tiampo ◽  
S. D. Mckinnon ◽  
J. A. Vallejos ◽  
W. Klein ◽  
...  
Keyword(s):  
Physical Meaning ◽  
Finite Time ◽  
Metastable Equilibrium ◽  
Lower Sensitivity ◽  
Time Interval ◽  
Finite Time Interval ◽  
Time Intervals ◽  
The Past ◽  
Local Clustering ◽  
Over Time

Abstract. The Thirulamai-Mountain (TM) metric was first developed to study ergodicity in fluids and glasses (Thirumalai and Mountain, 1993) using the concept of effective ergodicity, where a large but finite time interval is considered. Tiampo et al. (2007) employed the TM metric to earthquake systems to search for effective ergodic periods, which are considered to be metastable equilibrium states that are disrupted by large events. The physical meaning of the TM metric for seismicity is addressed here in terms of the clustering of earthquakes in both time and space for different sets of data. It is shown that the TM metric is highly dependent not only on spatial/temporal seismicity clustering, but on the past seismic activity of the region and the time intervals considered as well, and that saturation occurs over time, resulting in a lower sensitivity to local clustering. These results confirm that the TM metric can be used to quantify seismicity clustering from both spatial and temporal perspectives, in which the disruption of effective ergodic periods are caused by the agglomeration of events.

scholarly journals SYNTHESIZING THE LÜ ATTRACTOR BY PARAMETER-SWITCHING

2011 ◽  
Vol 21 (01) ◽  
pp. 323-331 ◽  
Author(s):  
MARIUS-F. DANCA
Keyword(s):  
Finite Time ◽  
Present Author ◽  
Control Parameter ◽  
Initial Value ◽  
Step Size ◽  
Time Intervals ◽  
Synthesis Algorithm ◽  
Finite Set ◽  
Parameter Values ◽  
Parameter Switching

In this letter we synthesize numerically the Lü attractor starting from the generalized Lorenz and Chen systems, by switching the control parameter inside a chosen finite set of values on every successive adjacent finite time intervals. A numerical method with fixed step size for ODEs is used to integrate the underlying initial value problem. As numerically and computationally proved in this work, the utilized attractors synthesis algorithm introduced by the present author before, allows to synthesize the Lü attractor starting from any finite set of parameter values.

scholarly journals Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
T. S. Doan ◽  
S. Siegmund
Keyword(s):  
Finite Time ◽  
Delay Equations ◽  
Volterra System ◽  
Time Intervals ◽  
Linear Delay ◽  
Diagonally Dominant ◽  
Coupling Terms

We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.

scholarly journals On the integral of geometric Brownian motion

2003 ◽  
Vol 35 (1) ◽  
pp. 159-183 ◽  
Author(s):  
Michael Schröder
Keyword(s):  
Brownian Motion ◽  
Integral Representation ◽  
Laplace Transform ◽  
Finite Time ◽  
Integral Representations ◽  
Geometric Brownian Motion ◽  
Bessel Processes ◽  
Time Intervals ◽  
The Laplace Transform ◽  
The Law

This paper studies the law of any real powers of the integral of geometric Brownian motion over finite time intervals. As its main results, an apparently new integral representation is derived and its interrelations with the integral representations for these laws originating by Yor and by Dufresne are established. In fact, our representation is found to furnish what seems to be a natural bridge between these other two representations. Our results are obtained by enhancing the Hartman-Watson Ansatz of Yor, based on Bessel processes and the Laplace transform, by complex analytic techniques. Systematizing this idea in order to overcome the limits of Yor's theory seems to be the main methodological contribution of the paper.

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