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By Mats Gyllenberg, Lars-Erik Persson

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Furthermore, some tools commonly employed in analyzing the behaviors of regular nonlinear dynamic systems are also needed in analyzing nonlinear piecewise-constant dynamic systems. Familiarity of the tools is important for analyzing the piecewise constant systems. In comparing with linear dynamic systems, the behaviors of nonlinear dynamic systems are much involved and complicated (Weaver et al. 1990, Strogatz 2000, Lakshmanan 2003). The typical features of the nonlinear dynamic systems can be described as the following: 1.

48, pp. 1013-1032, 2002. Zhang, B. , and Parhi, N. “Oscillatory and Nonoscillatory Properties of First Order Differential Equations with Piecewise Constant Deviating Arguments,” Journal of Mathematical Analysis and Applications, Vol. 139, pp. 23-25, 1989. 1. Introduction Before a thorough study on the methodology of solving and analyzing nonlinear piecewise constant systems, some fundamental knowledge on regular nonlinear dynamics systems and techniques for solving and analyzing the systems are necessary.

Discharging Capacitor Conductors, resistors and inductances are widely used for electrical circuits in electric engineering practice. 4. In the figure, C represents a conductor, R a resistor and L designates an inductance, as the convention and the three electric parts are connected in series. C, R and L also represent the quantities of capacitance, resistance and inductance respectively. Suppose that the electric parts are all perfectly connected and the fundamental electric laws such as Ohm’s law and Kichhoff ’s Law (Toro 1986) can be applied.

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