Preface During most of the Twentieth Century, physicists have been mainly concerned with linear dynamics. Despite the works of Poincaré, Birkhoff and von Neumann, the paradigm in physics was linear dynamics. Courses in Classical Mechanics systematically ignored intrinsically non-linear phenomena and chaos, restricting Mechanics to Integrable Systems, i.e., dynamical systems with an underlying L...

A sinusoidally-driven system with a simple signum nonlinearity term is investigated through an analytical analysis as well as dynamic simulation. To obtain the correct Lyapunov exponents, the signum function is replaced by a sharply varying continuous hyperbolic tangent function. By phase portraits, Poincaré sections and bifurcation diagrams, the rich dynamic behaviors of this system are demons...

A very simple nonlinear parallel nonautonomous LCR circuit with Chua’s diode as its only nonlinear element, exhibiting a rich variety of dynamical features, is proposed as a variant of the simplest nonlinear nonautonomous circuit introduced by Murali, Lakshmanan and Chua (MLC). By constructing a two-parameter phase diagram in the (F–ω) plane, corresponding to the forcing amplitude (F ) and freq...

Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titrati...

We present a simulation of a dripping faucet system. A new algorithm based on Lagrangian description is introduced. The shape of drop falling from a faucet obtained by the present algorithm agrees quite well with experimental observations. Long-term behavior of the simulation can reproduce period-one, period-two, intermittent and chaotic oscillations widely observed in experiments. Possible rou...