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- Ralf Eichhorn, Stefan J Linz, Peter Hä
- 1998

Third-order explicit autonomous differential equations in one scalar variable or, mechanically interpreted, jerky dynamics constitute an interesting subclass of dynamical systems that can exhibit many major features of regular and irregular or chaotic dynamical behavior. In this paper, we investigate the circumstances under which three dimensional… (More)

- J C Sprott, Stefan J Linz
- 2000

1 It came as a surprise to most scientists when Lorenz in 1963 discovered chaos in a simple system of three autonomous ordinary differential equations with two quadratic nonlinearities. This paper reviews efforts over the subsequent years to discover even simpler examples of chaotic flows. There is reason to believe that the algebraically simplest examples… (More)

- Stefan J Linz, J C Sprott
- 1999

Using an extensive numerical search for the simplest chaotic non-polynomial autonomous three-dimensional dynamical systems, we identify an elementary third-order diffential equation that contains only one control parameter and only one nonlinearity in the form of the modulus of the dynamical variable. We discuss general properties of this equation and the… (More)

The phenomenon of effective phase synchronization in stochastic oscillatory systems can be quantified by an average frequency and a phase diffusion coefficient. A different approach to compute the noise-averaged frequency is put forward. The method is based on a threshold crossing rate pioneered by Rice. After the introduction of the Rice frequency for… (More)

– Experimental results on amorphous ZrAlCu thin-film growth and the dynamics of the surface morphology as predicted from a minimal nonlinear stochastic deposition equation are analysed and compared. Key points of this study are: i) an estimation procedure for coefficients entering into the growth equation and ii) a detailed analysis and interpretation of… (More)

Third-order explicit autonomous dierential equations, commonly called jerky dynamics, constitute a powerful approach to understand the properties of functionally very simple but nonlinear three-dimensional dynamical systems that can exhibit chaotic long-time behavior. In this paper, we investigate the dynamics that can be generated by the two simplest… (More)

- Martin Raible, Stefan J Linz, Peter Hä
- 2000

A nonlinear stochastic growth equation is derived from ͑i͒ the symmetry principles relevant for the growth of vapor deposited amorphous films, ͑ii͒ no excess velocity, and ͑iii͒ a low-order expansion in the gradients of the surface profile. A growth instability in the equation is attributed to the deflection of the initially perpendicular incident particles… (More)

Lyapunov exponents represent important quantities to characterize the properties of dynamical systems. We show that the Lyapunov exponents of two dierent dynamical systems that can be converted to each other by a transformation of variables are identical. Moreover, we derive sucient conditions on the transformation for this invariance property to hold. In… (More)

A nonlinear stochastic growth equation for the spatiotemporal evolution of the surface morphology of amorphous thin films in the presence of potential density variations is derived from the relevant physical symmetries and compared to recent experimental results. Numerical simulations of the growth equation exhibit a saturation of the surface morphology for… (More)