204 research outputs found
Dynamical Systems on Leibniz Algebroids
In this paper we study the differential systems on Leibniz algebroids. We
introduce a class of almost metriplectic manifolds as a special case of Leibniz
manifolds. Also, the notion of almost metriplectic algebroid is introduced.
These types of algebroids are used in the presentation of associated
differential systems. We give some interesting examples of differential systems
on algebroids and the orbits of the solutions of corresponding systems are
established.Comment: 14 pages, 6 figures, the paper will be presented at The 5-th
Conference of Balkan Society of Geometers, August 29-September 2, 2005
Mangalia, Romani
Leibniz Dynamics with Time Delay
In this paper we show that several dynamical systems with time delay can be
described as vector fields associated to smooth functions via a bracket of
Leibniz structure. Some examples illustrate the theoretical considerations.Comment: 15 pages, 2 figures, it will be presented at The 5-th Conference of
Balkan Society of Geometers, August 29- September 2, 2005, Mangalia, Romani
Analysis of a 3D chaotic system
A 3D nonlinear chaotic system, called the T system, is analyzed in this
paper. Horseshoe chaos is investigated via the heteroclinic Shilnikov method
constructing a heteroclinic connections between the saddle equilibrium points
of the system. Partially numerical computations are carried out to support the
analytical results
Synchronization and secure communication using some chaotic systems of fractional differential equations
Using Caputo fractional derivative of order we
consider some chaotic systems of fractional differential equation. We will
prove that they can be synchronized and anti-synchronized using suitable
nonlinear control function. The synchronized or anti-synchronized error system
of fractional differential equations is used in secure communication.Comment: 10 pages, 6 figure
Stochastic generalized fractional HP equations and applications
In this paper we established the condition for a curve to satisfy stochastic
generalized fractional HP (Hamilton-Pontryagin) equations. These equations are
described using Ito integral. We have also considered the case of stochastic
generalized fractional Hamiltonian equations, for a hyperregular Lagrange
function. From the stochastic generalized fractional Hamiltonian equations,
Langevin generalized fractional equations were found and numerical simulations
were done.Comment: 14 pages, 10 figures, the paper will be presented at The
International Conference of Differential Geometry and Dynamical Systems
DGDS-2009/October 8-11, 2009, University Politehnica of Bucharest, Romani
Dissipative Mechanical Systems with Delay
The idea of dissipative mechanical system with delay is proposed. The paper
studies the phenomenon of dissipation with delay for Euler-Poincare systems on
Lie algebras or equivalently, for Lie-Poisson systems on the duals of Lie
algebras. The study was suggested by the work [2] and it is ended with a
discussion regarding the stability and the Hopf bifurcations for the free rigid
body with delay.Comment: 33 page
Rent seeking games with tax evasion
We consider the static and dynamic models of Cournot duopoly with tax
evasion. In the dynamic model we introduce the time delay and we analyze the
local stability of the stationary state. There is a critical value of the delay
when the Hopf bifurcation occurs.Comment: 8 pages, 4 figures, the paper was presented at Pannonian Applied
Mathematical Meetings, 31 may-3june, 200
A dynamic p53-mdm2 model with delay kernel
Specific activator and repressor transcription factors which bind to specific
regulator DNA sequences, play an important role in gene activity control.
Interactions between genes coding such transcripion factors should explain the
different stable or sometimes oscillatory gene activities characteristic for
different tissues. In this paper, the dynamic P53-Mdm2 interaction model with
distributed delays and weak kernel, is investigated. Choosing the delay or the
kernel's coefficient as a bifurcation parameter, we study the direction and
stability of the bifurcating periodic solutions. Some numerical examples are
finally given for justifying the theoretical results.Comment: 23 pages, 8 figures, the paper was presented at "Conference
Francophone sur la Modelisation Mathematique en Biologie et en Medecine",
Craiova, Roumanie,12-14 July, 200
Hopf bifurcation analysis of pathogen-immune interaction dynamics with delay kernel
The aim of this paper is to study the steady states of the mathematical
models with delay kernels which describe pathogen-immune dynamics of many kinds
of infectious diseases. In the study of mathematical models of infectious
diseases it is important to predict whether the infection disappears or the
pathogens persist. The delay kernel is described by the memory function that
reflects the influence of the past density of pathogen in the blood.
By using the coefficient of kernel k, as a bifurcation parameter, the models
are found to undergo a sequence of Hopf bifurcation. The direction and the
stability criteria of bifurcation periodic solutions are obtained by applying
the normal form theory and the center manifold theorems. Some numerical
simulation examples for justifying the theoretical results are also given.Comment: 18 pages, 12 figures, the paper was presented at "Conference
Francophone sur la Modelisation Mathematique en Biologie et en Medecine",
Craiova, Roumanie,12-14 July, 200
The analysis of stochastic stability of stochastic models that describe tumor-immune systems
In this paper we investigate some stochastic models for tumor-immune systems.
To describe these models, we used a Wiener process, as the noise has a
stabilization effect. Their dynamics are studied in terms of stochastic
stability in the equilibrium points, by constructing the Lyapunov exponent,
depending on the parameters that describe the model. Stochastic stability was
also proved by constructing a Lyapunov function. We have studied and and
analyzed a Kuznetsov-Taylor like stochastic model and a Bell stochastic model
for tumor-immune systems. These stochastic models are studied from stability
point of view and they were represented using the second Euler scheme and Maple
12 software.Comment: 23 pages, 30 figure
- …