Perturbations and Hopf bifurcation of the planar discontinuous dynamical system

The objective of the paper is to obtain results on the behavior of a specific plane discontinuous dynamical system in the neighbourhood of the singular point. A new technique of investigation is presented. Conditions for existence of the foci and centres are proposed. The focus-centre problem and Hopf bifurcation are considered. Appropriate examples are given to ilustrate the bifurcation theorem.


IDER, SK (1996-01-03)
In this paper inverse dynamics of redundant multibody systems using a minimum number of control forces is formulated. It is shown that the control forces and the task accelerations may become noncausal at certain configurations, yielding the dynamical equation set of the system to be singular. For a given set of tasks, each different set of actuators leads to a different system motion and also to different singular configurations. To avoid the singularities in the numerical solution, the dynamical equations...
Discontinuous dynamics with grazing points
Akhmet, Marat (2016-09-01)
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of solutions are thoroughly analyzed. A variational system around a grazing solution which depends on near solutions is constructed. Orbital stability of grazing cycles is examined by linearization. Small parameter method is extended for analysis of grazing orbits, and bifurcation of cycles is observed in an example. Linearization around an equilibrium grazing point ...
Acceleration of line of sight analysis algorithms with parallel programming
Yılmaz, Gökhan; Sürer, Elif; Temizel, Alptekin (null; 2017-11-23)
Line of sight (LOS) analysis is a set of methods and algorithms to determine the visible points in a terrain with reference to a specific observer point. This analysis is used in simulations, Geographic Information System (GIS) applications and games. For this reason, it is important to have a capability to get results quickly and facilitate analysis in such a way that the interaction with the changing reference points is possible. Van Kreveld, R2 and R3 are the most frequently used algorithms in line of si...
Almost periodic solutions of the linear differential equation with piecewise constant argument
Akhmet, Marat (2009-10-01)
The paper is concerned with the existence and stability of almost periodic solutions of linear systems with piecewise constant argument where t∈R, x ∈ Rn [·] is the greatest integer function. The Wexler inequality [1]-[4] for the Cauchy's matrix is used. The results can be easily extended for the quasilinear case. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Copyright © 2009 Watam Press.
Stability criteria for linear periodic impulsive Hamiltonian systems
Guseinov, G. Sh.; Zafer, Ağacık (2007-11-15)
In this paper we obtain stability criteria for linear periodic impulsive Hamiltonian systems. A Lyapunov type inequality is established. Our results improve also the ones previously obtained for systems without impulse effect. (c) 2007 Elsevier Inc. All rights reserved.
Citation Formats
M. Akhmet, “Perturbations and Hopf bifurcation of the planar discontinuous dynamical system,” NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, pp. 163–178, 2005, Accessed: 00, 2020. [Online]. Available: