MATHEMATICAL RESEARCHES
Year:2017 | Volume:3 | Issue:2 |Papers Count:7

In this paper we consider a continues Lorenz – type dynamical system. Dynamical behaviors of this system such as computing equilibrium points, different bifurcation curves and computation of normal form coefficient of each bifurcation point analytically and numerically. In particular we derived sufficient conditions for existence of Hopf and Pitchfork bifurcations and determined criticality of these bifurcations. By means of numerical simulations, we show that the system may have chaotic behavior under some conditions. By employing numerical continuation method, we first compute bifurcation curves and then compute all codimension 1 and 2 bifurcation along these curves with determined of the corresponding normal form coefficient.

projective Ricci curvature. Then we characterize isotropic projective Ricci curvature of Randers metrics. we also show that Randers metrics are PRic-reversible if and only if they are PRic-quadratic.

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In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied.  In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every (a, b)-metric of non-zero constant flag curvature and non-zero relatively isotropic stretch curvature on a manifold of dimension n>2 has a constant characteristic scalar along the geodesics. Two dimensional Finsler manifolds of relatively stretch curvature are studied, too.

The main purpose of this paper is to introduce the rotation number for non-autonomous and iterated function systems. First, we define iterated function systems and the lift of these types of systems on the unit circle. In the following, we define the rotation number and investigate the conditions of existence and uniqueness of this number for our systems. Then, the notions rotational entropy and rotational shadowing have been considered and some basic properties of these notions in the iterated function and non-autonomous systems have been investigated.

We chracterize orbit spaces and orbits of cohomogeneity two isometric actions on hyperbolic spaces.

Gompertz-Poisson distribution is a three-parameter lifetime distribution with increasing, decreasing, increasing-decreasing and unimodal shape failure rate function and a composition of Gompertz and Poisson distributions cut at zero point that in this paper estimated the parameters of the distribution by maximum likelihood method and in order to confirm the calculated estimates, based on random sample with volumes of 100, 200, 300, 400 and 500 of Gompertz-Poisson distribution simulation study was conducted. Also with the help of two real data sets and comparing Gompertz-Poisson distribution with several other distributions of lifetime we show this distribution is a good model for data fitness related to lifetime.