Two Characteristic Behavior Of Piecewise Continuous Systems: V-type Intermittency Prelude To The Lock-in Ladder And Semi-dissipative,

This thesis reports a study on the characteristics of some piecewise-smooth classical systems. The systems studied are a model of an RLC circuit with an analogy switch and a model of an electronic circuit with over-voltage protection and a dissipative element.It is discovered in the RLC circuit model that type V intermittency becomes the main route of the transition from periodic motion to chaos. This type of intermittency can happen only in piecewise-smooth dissipative systems. In addition to the known characteristics of type V intermittency, such as the mechanism of the border-collision bifurcation and the logarithmic scaling behavior of the averaged laminar lengths, a new characteristic of type V iritermittency discovered in this system is the so-called "prelude phase-locking staircase to type V intermittency", which does not show the traditional devil's staircase form. In discontinuous maps, in general a periodic orbit, after losing its stability via a type V intermittency, can transmit to chaos only after a sequence of higher period orbits. The characteristic quantity (like the "transfer number" defined in this thesis) that describes the higher period orbits forms a sequence of phase-locked steps on the plane formed by it and the control parameter. All the phase-locked steps form a so-called prelude phase-locking staircase to type V intermittency. All such staircases discovered before have the form of the traditional devil's staircase. This is the first time to observe a prelude phase-locking staircase to type V intermittency with other forms. In order to verify these numerical results, we analytically obtained the end positions of the phase-locked steps those have the transfer number 1/n and found a good agreement with the numerical results. Our numerical investigation also indicates that the chaotic attractor appeared after the prelude phase-locking staircase was end-result of the set of the images of the discontinuous border of the system function. This seems to be a common feature of the chaotic attractors those appear after the prelude phase-locking staircase in the system.The model of electronic circuit is described by a piecewise-continuous concatenation of a dissipative map and a conservative map, which is addressed as a "semi-dissipative system". The system can show the so-called quasi-dissipative properties caused by the noninvertibility that is induced by the discontinuity of the mapping, the traditional dissipative properties caused by the dissipative sub-map, as well as the so-called "mixed-dissipative property" caused by the mixture of them. Usually the area in parameter space, in phase-space and in the types of phenomena where traditional dissipative properties or quasi-dissipative properties dominate is confined, but the confined behavior often shows a great influence on the characteristics of the system. The system's behavior usually is determined by the mixed dissipative properties in a long time or large ranges. This is one of the basic features of semi-dissipative systems. Another characteristic different from quasi-dissipative systems concerns the iteration gap. There is a piece of gap in the phase plane that is induced by dissipative property. It confines the "escaping hole" in a so-called "semi-dissipative crisis", which owns two particular properties: 1. The mechanism of the crisis is the sudden appearance of a periodic orbit with mixed-dissipative property inside a chaotic quasi-attractor; 2. The escaping hole can be defined as the area completely dominated by traditional dissipative property that is confined by the dissipative-induced gap. To our knowledge, such a crisis has never been observed yet.