Lyapunov-Type Inequalities for Nonlinear Differential Systems

2021 ◽  
pp. 189-292
Author(s):  
Ravi P. Agarwal ◽  
Martin Bohner ◽  
Abdullah Özbekler
Keyword(s):  
Differential Systems ◽  
Nonlinear Differential Systems

Transformation of non-Gaussian random processes, signals and noise in the nonlinear differential systems by the method of cumulative functions

2018 ◽  
Vol 15 (1) ◽  
pp. 84-93
Author(s):  
V. I. Volovach ◽  
V. M. Artyushenko
Keyword(s):  
Spectral Characteristics ◽  
Random Processes ◽  
Spectral Densities ◽  
Differential Systems ◽  
Non Gaussian ◽  
Nonlinear Differential Systems

Reviewed and analyzed the issues linked with the torque and naguszewski cumulant description of random processes. It is shown that if non-Gaussian random processes are given by both instantaneous and cumulative functions, it is assumed that such processes are fully specified. Spectral characteristics of non-Gaussian random processes are considered. It is shown that higher spectral densities exist only for non-Gaussian random processes.

scholarly journals ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF NONLINEAR DIFFERENTIAL SYSTEMS

1993 ◽  
Vol 24 (2) ◽  
pp. 173-188
Author(s):  
LIHONG HUANG ◽  
JIANSHE YU
Keyword(s):  
Periodic Solutions ◽  
Special Form ◽  
Differential Systems ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions ◽  
Nonlinear Differential Systems

In this paper three theorems on the existence of nontrivial periodic solutions of the system \[ dx/dt =e(y)\]\[dy/dt =-e(y)f(x)- g(x)\] are proved, which not only generalize some known results on the existence of periodic solutions of Lienard's system (i.e. the special form for $e(y) = y$), but also relax or eliminate some traditional assumptions.

scholarly journals The Stability of Nonlinear Differential Systems with Random Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Josef Diblík ◽  
Irada Dzhalladova ◽  
Miroslava Růžičková
Keyword(s):  
Trivial Solution ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
New Method ◽  
Random Parameters ◽  
Differential Systems ◽  
The Stability ◽  
Nonlinear Differential Systems

The paper deals with nonlinear differential systems with random parameters in a general form. A new method for construction of the Lyapunov functions is proposed and is used to obtain sufficient conditions forL2-stability of the trivial solution of the considered systems.

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