Analysis of nonlinear autonomous systems has been a popular field of study in recent decades. As an interesting nonlinear behavior, chaotic dynamics has been intensively investigated since Lorenz discovered the first physical evidence of chaos in his famous equations. Although many chaotic systems have been ever reported in the literature, a systematic and qualitative approach for chaos generat...

Barnsley (2006) used chaos game in function systems and it gave rise to interesting fractals by combining it with function iterations. A fractal fern is generated by taking different probabilities in the chaos game. In this paper, we introduce two advanced iterations from nonlinear analysis into the study of IFS for generation and pattern recognition of new fractal ferns. Gottfried (1991), and ...

We analyse a simple model of a digitally controlled mechanical system, which may perform chaotic vibrations. As a consequence of the digital effects, i.e., the sampling and the round-off error, the behaviour of this system can be described by the socalled micro-chaos map. If dry friction is present in the system, it can stop the motion. In such cases the resulting behaviour is referred to as tr...

We use exact diagonalization to study energy level statistics and out-of-time-order correlators (OTOCs) for the simplest supersymmetric extension $\hat{H}_S = \hat{H}_B \otimes I + \hat{x}_1 \sigma_1 \hat{x}_2 \sigma_3$ of bosonic Hamiltonian $\hat{H}_B \hat{p}_1^2 \hat{p}_2^2 \hat{x}_1^2 \, \hat{x}_2^2$. For a long time, this was considered one systems which exhibit dynamical chaos both classi...

Based on a new first-order nonlinear ordinary differential equation with a sixth-degree nonlinear term and some of its special solutions, a generalized transformation method is proposed to obtain more general exact solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky equations. As a result, new exact nontravelling wave solutions are obtained including soliton-like solutions and trigonomet...

We demonstrate deterministic extensive chaos in the dynamics of large sparse networks of theta neurons in the balanced state. The analysis is based on numerically exact calculations of the full spectrum of Lyapunov exponents, the entropy production rate, and the attractor dimension. Extensive chaos is found in inhibitory networks and becomes more intense when an excitatory population is include...