Zuohuan Zheng

Nonlinear coupling between thermal mass and natural ventilation in buildings

An ideal naturally ventilated building model that allows a theoretical study of the effect of thermal mass associating with the non-linear coupling between the airflow rate and the indoor air temperature is proposed. When the ventilation rate is constant, both the phase shift and fluctuation of the indoor temperature are determined by the time constant of the system and the dimensionless convective heat transfer number. When the ventilation rate is a function of indoor and outdoor air temperature difference, the thermal mass number and the convective heat transfer air change parameter are suggested. The new thermal mass number measures the capacity of heat storage, rather than the amount of thermal mass. The analyses and numerical results show that the non-linearity of the system does neither change the periodic behaviour of the system, nor the behaviour of phase shift of the indoor air temperature when a periodic outdoor air temperature profile is considered. The maximum indoor air temperature phase shift induced by the direct outdoor air supply without control is 6 h.

Random periodic solutions of random dynamical systems

Abstract In this paper, we give the definition of the random periodic solutions of random dynamical systems. We prove the existence of such periodic solutions for a C 1 perfect cocycle on a cylinder using a random invariant set, the Lyapunov exponents and the pullback of the cocycle.

Generating two simultaneously chaotic attractors with a switching piecewise-linear controller

It has been demonstrated that a piecewise-linear system can generate chaos under suitable conditions. This paper proposes a novel method for simultaneously creating two symmetrical chaotic attractor––an upper-attractor and a lower-attractor––in a 3D linear autonomous system. Basically dynamical behaviors of this new chaotic system are further investigated. Especially, the chaos formation mechanism is explored by analyzing the structure of fixed points and the system trajectories.

The complicated trajectory behaviors in the Lorenz equation

Abstract In this paper, trajectories of the Lorenz equation are analyzed in details. In particular, it is rigorously proved that all nontrivial trajectories travel through two special Poincare projections with infinitely many times. The result would describe the structure of the Lorenz attractor from a lateral aspect.

Dynamical behavior in the modeling of cell division cycle

Abstract In this paper we qualitatively analyze mathematical modeling of the cell division cycle established by Novak and Tyson (Novak B, Tyson JJ. J Theor Biol 1993;165:101–34) and discuss the existence, uniqueness, stability and unstability of its singular point and the system boundedness, existence and nonexistence of closed orbit and its global structure.

HOMOCLINIC SHADOWING AND ITS APPLICATION TO CHAOTIC SYSTEMS

In our paper, by using shadowing techniques, we develop a general method for establishing the existence of a transversal homoclinic orbit to a periodic orbit of

Semi-uniform sub-additive ergodic theorems for discontinuous skew-product transformations

C_{\rm Lip}^{1}

Global structure for a class of dynamical systems

diffeomorphisms in Rn which implies the occurrence of chaos.

NONLINEAR RESONANCE AND QUASI-PERIODIC SOLUTIONS FOR VENTILATION FLOWS IN A SINGLE OPENING ENCLOSURE

In this paper we will establish some semi-uniform ergodic theorems for skew-product transformations with discontinuity from the point of view of topology. The main assumptions are that the discontinuity sets of transformations are neglected in some measure-theoretical sense. The theorems have extended the classical results which have been established for continuous dynamical systems.

Existence of echo wave in the coupled-Oregonator system ☆

Abstract In this paper, we shall consider the global structure of positive bounded systems on the plane which have m singular points, but not any closed orbits and singular closed orbits. We shall prove that these systems have at least m −1 connecting orbits; and all the connecting orbits, homoclinic orbits and singular points constitute a compact simply connected set. Each of other orbits tends to a singular point as t →+∞, and approaches to the infinity as t →−∞.