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• We the dynamics of freely vibrating guitar strings. • We use methods of nonlinear time series analysis. • We show how false results can be mistaken as proof of deterministic chaos. • We show how to avoid false claims of chaos in vibrating strings. • We note the applicability of our approach in classrooms and for other musical instruments. The determination of properties of nonlinear dynamics from recorded time series offers fascinating insights into everyday phenomena that can be explored in the lab as well as in physics classrooms. A noteworthy challenge thereby is the distinction between multirhythmic signals, i.e., time series with many but still a finite number of harmonic frequencies, and deterministically chaotic signals. Especially if the signals are relatively short and decaying in intensity, both can have very similar continuous Fourier transforms. We show that stringed instruments offer easily accessible waveforms that can be studied with methods of nonlinear time series analysis to demonstrate that even highly multirhythmic signals can be robustly distinguished from deterministic chaos. In particular, we study the transition from sounds to chords by means of recordings of picked guitar strings, showing how the increasing complexity of the waveforms is still in fact periodic although it might seem chaotic. The treatment is instructive in terms of identifying common pitfalls that are associated with declaring deterministic chaos in observed data, and since it relies on readily available resources, it seems particularly well suited for the classroom on nonlinear dynamics and time series analysis. [ABSTRACT FROM AUTHOR]

Highlights • Design of a minimal digital chaotic system. • A digit complement is used for the design. • The number of necessary logic elements is significantly reduced. • The system can be implemented on reconfigurable hardware. Abstract Over the past few decades, many works have been devoted to designing simple chaotic systems based on analog electronic circuits. However, the same attention is not observed in digital chaotic systems. This paper presents a design of a digital chaotic system using a digit complement. This special case of fixed-point number representation allows us to reduce the silicon area and the number of logic elements to perform the arithmetic operations. The design presents a configurable number of bits, and it is based on the logistic map. The proposed circuit has been implemented on a reconfigurable hardware, FPGA Cyclone V, showing that the number of logic elements has been significantly reduced compared to other works in the literature. [ABSTRACT FROM AUTHOR]

• Finance and economics are complex nonlinear systems, affected by various external factors. • We study the dynamics and complexity in a fractional-order financial system with time delays. • We observe fascinating transitions to deterministic chaos, including cascading period doubling. • Complexity is particularly high in response to variations of derivative orders. • Derivative orders are identified as key system parameters. Finance and economics are complex nonlinear systems that are affected by various external factors, including of course human action, bilateral relations, conflicts, and policy. Time delays in a financial system take into account the amount of time that passes from a particular policy or decision being made to it actually taking effect. It is thus important to consider time delays as an integral part of modeling in this field. Moreover, many features of financial systems cannot be expressed sufficiently precisely by means of integer-order calculus. Fractional-order calculus alleviates these shortcomings. The aim of this paper is therefore to study the dynamics and complexity in a fractional-order financial system with time delays. We observe fascinating transitions to deterministic chaos, including cascading period doubling, as well as high levels of complexity. This is particularly true in response to variations of derivative orders, which are thus identified as key system parameters. [ABSTRACT FROM AUTHOR]