On quadratic symplectic mappings.
On some dynamical properties of S-unimodal maps on an interval
On the Bautin bifurcation for systems of delay differential equations.
On the bifurcation set of complex polynomial with isolated singularities at infinity
On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance
On the critical periods of Liénard systems with cubic restoring forces.
On the dynamics of a delayed SIR epidemic model with a modified saturated incidence rate.
On the dynamics of polynomial-like mappings
On the existence and stability of unfoldings of equivariant two-parameter bifurcation problems.
On the existence of a periodic solution of a nonlinear ordinary differential equation.
On the existence of bright solitons in cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity.
On the existence of chaotic behaviour of diffeomorphisms
For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.
On the existence of homoclinic points
On the existence of Hopf bifurcation in an open economy model
On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors
We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations...
On the prescribed-period problem for autonomous Hamiltonian systems.
On the principle of stability of invariance of physical systems
On vanishing inflection points of plane curves
We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs which take into account the inflection points of the fibres of . We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.
One-Parameter Bifurcation Analysis of Dynamical Systems using Maple
This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.* This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–359/2008.
One-parameter family of cubic Kolmogorov system with an isochronous center.
We show the existence of a one-parameter family of cubic Kolmogorov system with an isochronous center in the realistic quadrant.