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Dynamics analysis and robust modified function projective synchronization of Sprott E system with quadratic perturbation

Zhen Wang, Wei Sun, Zhouchao Wei, Xiaojian Xi (2014)

Kybernetika

Hopf bifurcation, dynamics at infinity and robust modified function projective synchronization (RMFPS) problem for Sprott E system with quadratic perturbation were studied in this paper. By using the method of projection for center manifold computation, the subcritical and the supercritical Hopf bifurcation were analyzed and obtained. Then, in accordance with the Poincare compactification of polynomial vector field in R 3 , the dynamical behaviors at infinity were described completely. Moreover, a...

Dynamics for a discrete competition and cooperation model of two enterprises with multiple delays and feedback controls

Lin Lu, Yi Lian, Chaoling Li (2017)

Open Mathematics

This paper is concerned with a competition and cooperation model of two enterprises with multiple delays and feedback controls. With the aid of the difference inequality theory, we have obtained some sufficient conditions which guarantee the permanence of the model. Under a suitable condition, we prove that the system has global stable periodic solution. The paper ends with brief conclusions.

Dynamics in a discrete predator-prey system with infected prey

Changjin Xu, Peiluan Li (2014)

Mathematica Bohemica

In this paper, a discrete version of continuous non-autonomous predator-prey model with infected prey is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions for the existence and global asymptotical stability of positive periodic solution of difference equations in consideration are established. An example shows the feasibility of the main results.

Dynamics of a two sex population with gestation period

Giorgio Busoni, Andrzej Palczewski (2000)

Applicationes Mathematicae

We investigate a mathematical model of population dynamics for a population of two sexes (male and female) in which new individuals are conceived in a process of mating between individuals of opposed sexes and their appearance is postponed by a period of gestation. The model is a system of two partial differential equations with delay which are additionally coupled by mathematically complicated boundary conditions. We show that this model has a global solution. We also analyze stationary ('permanent')...

Dynamics of systems with Preisach memory near equilibria

Stephen McCarthy, Dmitrii Rachinskii (2014)

Mathematica Bohemica

We consider autonomous systems where two scalar differential equations are coupled with the input-output relationship of the Preisach hysteresis operator, which has an infinite-dimensional memory. A prototype system of this type is an LCR electric circuit where the inductive element has a ferromagnetic core with a hysteretic relationship between the magnetic field and the magnetization. Further examples of such systems include lumped hydrological models with two soil layers; they can also appear...

Dynamics of the tumor-immune system competition - the effect of time delay

Magda Galach (2003)

International Journal of Applied Mathematics and Computer Science

The model analyzed in this paper is based on the model set forth by V.A. Kuznetsov and M.A. Taylor, which describes a competition between the tumor and immune cells. Kuznetsov and Taylor assumed that tumor-immune interactions can be described by a Michaelis-Menten function. In the present paper a simplified version of the Kuznetsov-Taylor model (where immune reactions are described by a bilinear term) is studied. On the other hand, the effect of time delay is taken into account in order to achieve...

Dynamics of Tuberculosis: The effect of Direct Observation Therapy Strategy (DOTS) in Nigeria

D. Okuonghae, A. Korobeinikov (2010)

Mathematical Modelling of Natural Phenomena

This paper presents mathematical models for tuberculosis and its dynamics under the implementation of the direct observation therapy strategy (DOTS) in Nigeria. The models establish conditions for the eradication of tuberculosis in Nigeria based on the fraction of detected infectious individuals placed under DOTS for treatment. Both numerical and qualitative analysis of the models were carried out and the effect of the fraction of detected cases of active TB on the various epidemiological classes...

Dynamics on Character Varieties and Malgrange irreducibility of Painlevé VI equation

Serge Cantat, Frank Loray (2009)

Annales de l’institut Fourier

We consider representations of the fundamental group of the four punctured sphere into SL ( 2 , ℂ ) . The moduli space of representations modulo conjugacy is the character variety. The Mapping Class Group of the punctured sphere acts on this space by symplectic polynomial automorphisms. This dynamical system can be interpreted as the monodromy of the Painlevé VI equation. Infinite bounded orbits are characterized: they come from SU ( 2 ) -representations. We prove the absence of invariant affine structure (and invariant...

Dynamique et formes normales d’équations différentielles implicites

Julien Aurouet (2014)

Annales de l’institut Fourier

Dans cet article on cherche à comprendre la dynamique locale d’équations différentielles implicites de la forme F ( x , y , d y ) = 0 , où F est un germe de fonction sur 𝕂 n × 𝕂 × 𝕂 n * (où 𝕂 = ℝ ou ℂ ), au voisinage d’un point singulier. Pour cela on utilise la relation intime entre les systèmes implicites et les champs liouvilliens. La classification par transformation de contact des équations implicites provient de la classification symplectique des champs liouvilliens. On utilise alors toute la théorie des formes normales pour les...

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