‎in this paper‎, ‎we have investigated the chaotic behavior of thermal convection in couple stress liquid saturated porous layer subject to gravity‎, ‎heated from below and cooled from above‎, ‎based on theory of dynamical system‎. ‎a low dimensional lorenz‎- ‎like model is obtained by using galerkin-truncation approximation‎. ‎we found that there is proportional relation between scaled couple ...

Abstract—New physical insights into the nonlinear Lorenz equations related to flow resistance is discussed in this work. The chaotic dynamics related to Lorenz equations has been studied in many papers, which is due to the sensitivity of Lorenz equations to initial conditions and parameter uncertainties. However, the physical implication arising from Lorenz equations about convectional motion a...

A modified form of the Townsend equations for the fluctuating velocity wave vectors is applied to a laminar three-dimensional boundary-layer flow. These equations are cast into a Lorenz-type system of equations. The initial system of Lorenz equations yields the generation of masked output signals containing internal ordered regions. The selfsynchronizing property of the Lorenz system of equatio...

The route to chaos as the pump power is raised in the Lorenz-like 15 N H 3 laser is studied using transients and compared with the route which is expected in the Lorenz Haken equations. The differences between the routes to chaos, as normally displayed by the experimental system and the Lorenz Haken equations, is described in terms of the bifurcations experienced in each system. It is also show...

where x and y ace co~aplex and z is real. The complex parameters r and a are defined by r = rl + it,,: a = 1 ie and o" and b are real. Behaviour ~markab ly different from the real Lo~,~nz model occurs. Only the origin is a fixed point except for the ~pecial case e + ~ = 0. We have been able to determine analytically two critical values of rt, namely r~ and rb. The or ion is a stable fixed point...

Resumen We first study the existence and uniqueness of strong solutions of a three dimensional system of globally modified Navier-Stokes equations with delay in the locally Lipschitz case. The asymptotic behaviour of solutions, and the existence of pullback attractor are also analyzed.

We present an algorithm for computing rigorous solutions to a large class of ordinary differential equations. The main algorithm is based on a partitioning process and the use of interval arithmetic with directed rounding. As an application, we prove that the Lorenz equations support a strange attractor, as conjectured by Edward Lorenz in 1963. This conjecture was recently listed by Steven Smal...

were derived by Edward Lorenz in 1963 as an over-simplified model of convection rolls within the atmosphere [1]. These coupled differential equations appear quite harmless; only two terms appear that cause non-linearity. Lorenz found, however, that the behavior of the system changed drastically over a wide range of parameters. For certain parameter values, Lorenz discovered that the system exhi...