Hopf bifurcation for a 3D filippov system

2009-12-01
Akhmet, Marat
Aruǧaslan, D.
Turan, M.
We study the behaviour of solutions for a 3-dimensional system of differential equations with discontinuous right hand side in the neighbourhood of the origin. Using B- equivalence of that system to an impulsive differential equation [3, 4], existence of a center manifold is proved, and then a Hopf bifurcation theorem is provided for such equations in the critical case. The results are apparently obtained for the systems with dimensions greater than two for the first time. Finally, an appropriate example is given to illustrate our results. Copyright © 2009 Watam Press.
Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

Suggestions

The finite element method over a simple stabilizing grid applied to fluid flow problems
Aydın, Selçuk Han; Tezer-Sezgin, Münevver; Department of Scientific Computing (2008)
We consider the stabilized finite element method for solving the incompressible Navier-Stokes equations and the magnetohydrodynamic (MHD) equations in two dimensions. The well-known instabilities arising from the application of standard Galerkin finite element method are eliminated by using the stabilizing subgrid method (SSM), the streamline upwind Petrov-Galerkin (SUPG) method, and the two-level finite element method (TLFEM). The domain is discretized into a set of regular triangular elements. In SSM, the...
Periodic solutions and stability of differential equations with piecewise constant argument of generalized type
Büyükadalı, Cemil; Akhmet, Marat; Department of Mathematics (2009)
In this thesis, we study periodic solutions and stability of differential equations with piecewise constant argument of generalized type. These equations can be divided into three main classes: differential equations with retarded, alternately advanced-retarded, and state-dependent piecewise constant argument of generalized type. First, using the method of small parameter due to Poincaré, the existence and stability of periodic solutions of quasilinear differential equations with retarded piecewise constant...
Inverse problems for a semilinear heat equation with memory
Kaya, Müjdat; Çelebi, Okay; Department of Mathematics (2005)
In this thesis, we study the existence and uniqueness of the solutions of the inverse problems to identify the memory kernel k and the source term h, derived from First, we obtain the structural stability for k, when p=1 and the coefficient p, when g( )= . To identify the memory kernel, we find an operator equation after employing the half Fourier transformation. For the source term identification, we make use of the direct application of the final overdetermination conditions.
Lyapunov-type inequalities for nonlinear impulsive systems with applications
Kayar, Zeynep; Zafer, Agacik (University of Szeged, 2016)
We obtain new Lyapunov-type inequalities for systems of nonlinear impulsive differential equations, special cases of which include the impulsive Emden-Fowler equations and half-linear equations. By applying these inequalities, sufficient conditions are derived for the disconjugacy of solutions and the boundedness of weakly oscillatory solutions.
Studies on the perturbation problems in quantum mechanics
Koca, Burcu; Taşeli, Hasan; Department of Mathematics (2004)
In this thesis, the main perturbation problems encountered in quantum mechanics have been studied.Since the special functions and orthogonal polynomials appear very extensively in such problems, we emphasize on those topics as well. In this context, the classical quantum mechanical anharmonic oscillators described mathematically by the one-dimensional Schrodinger equation have been treated perturbatively in both finite and infinite intervals, corresponding to confined and non-confined systems, respectively.
Citation Formats
M. Akhmet, D. Aruǧaslan, and M. Turan, “Hopf bifurcation for a 3D filippov system,” Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, vol. 16, no. 6, pp. 759–775, 2009, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=73249146222&origin=inward.