Shape Memory Alloy (SMA) dynamical systems may exhibit a rich response that can include periodic, quasi-periodic, chaotic and hyperchaotic behaviors. In this regard, diagnostic tools are important in order to identify the different types of behaviors. This paper aims to analyze systems with SMA elements through a nonlinear dynamics perspective with a specific focus on the use of 0–1 test to quantify the chaoticity of the dynamical response of SMA oscillators. The investigation includes different constitutive models for the restitution force on both single- and two-degree of freedom oscillators. Results of the 0–1 test are compared with Lyapunov exponents calculated with different algorithms. The analyses show that the 0–1 test can be considered a reliable and computationally efficient alternative as a diagnostic tool of chaotic responses

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Abstract. The mathematical modeling of ecological phenomena may describe time evolution and spatial distribution being capable to explain some important characteristics of ecological systems. Although there are many difficulties related to the system description, their modeling may define at least a system caricature, which may be useful for different goals. This contribution deals with the modeling of the global warming in a nonlinear dynamics point of view. Mathematical modeling is based on the daisyworld that is able to describe the global regulation that can emerge from the interaction between life and environment. In brief, daisyworld represents life by daisy populations while the environment is represented by temperature. Here, two daisy populations are of concern, black and white daisies, and an extra variable related to greenhouse gases is incorporated in the model allowing the analysis of the global warming. Moreover, transient analysis of temperature evolution is of concern. Climate variability is represented by a sinusoidal variation of the luminosity. Numerical simulations are investigated in order to present a qualitative description of the phenomenon. Daisyworld dynamics presents a rich behavior including chaos.

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