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Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents’ spectrum, and entropy measurement. Bifurcation analysis of the proposed system with two initiation methods reveals its multistability. As an engineering application, the system’s efficiency is tested in image encryption. The complexity of the chaotic attractor of the proposed system makes it a proper choice for encryption. States of the chaotic attractor are used to shuffle the rows and columns of the image, and then the shuffled image is XORed with the states of chaotic attractor. The unpredictability of the chaotic attractor makes the encryption method very safe. The performance of the encryption method is analyzed using the histogram, correlation coefficient, Shannon entropy, and encryption quality. The results show that the encryption method using the proposed chaotic system has reliable performance.

In this paper a modified third order Wien bridge oscillator with fractional order memristor is proposed. Various dynamical properties of the proposed oscillator are investigated such as equilibrium points, Eigenvalues, Lyapunov exponents and bifurcation diagrams. The Lyapunov spectrum of the system for various values of fractional order is derived. Using forward and backward continuation methods of plotting bifurcation diagram, the multistability of the oscillator is investigated. The proposed oscillator is realized using Field Programmable Gate Arrays and the experiment is conducted using hardwaresoftware co-simulation.

Perpetual Points (PPs) have been introduced as an interesting new topic in nonlinear dynamics, and there is a hypothesis that these points can determine whether a system is dissipative or not. This paper demonstrates that this hypothesis is not true since there are counterexamples. Furthermore, we explain that it is impossible to determine dissipation of a system based only on the structure of the system and its equations.

Perpetual Points (PPs) have been introduced as an interesting new topic in nonlinear dynamics, and there is a conjecture that these points can be used to find hidden attractors. This note demonstrates some examples where PPs cannot locate their hidden attractors.

Coronavirus disease 2019 is a recent strong challenge for the world. In this paper, an epidemiology model is investigated as a model for the development of COVID-19. The propagation of COVID-19 through various sub-groups of society is studied. Some critical parameters, such as the background of mortality without considering the disease state and the speed of moving people from infected to resistance, affect the conditions of society. In this paper, early warning indicators are used to predict the bifurcation points in the system. In the interaction of various sub-groups of society, each sub-group can have various parameters. Six cases of the sub-groups interactions are studied. By coupling these sub-groups, various dynamics of the whole society are investigated.

Classical indicators of tipping points have limitations when they are applied to an ecological and a biological model. For example, they cannot correctly predict tipping points during a period-doubling route to chaos. To counter this limitation, we here try to modify four well-known indicators of tipping points, namely the autocorrelation function, the variance, the kurtosis, and the skewness. In particular, our proposed modification has two steps. First, the dynamic of the considered system is estimated using its time-series. Second, the original time-series is divided into some sub-time-series. In other words, we separate the time-series into different period-components. Then, the four different tipping point indicators are applied to the extracted sub-time-series. We test our approach on an ecological model that describes the logistic growth of populations and on an attention-deficit-disorder model. Both models show different tipping points in a period-doubling route to chaos, and our approach yields excellent results in predicting these tipping points.

Critical slowing down is considered to be an important indicator for predicting critical transitions in dynamical systems. Researchers have used it prolifically in the fields of ecology, biology, sociology, and finance. When a system approaches a critical transition or a tipping point, it returns more slowly to its stable attractor under small perturbations. The return time to the stable state can thus be used as an index, which shows whether a critical change is near or not. Based on this phenomenon, many methods have been proposed to determine tipping points, especially in biological and social systems, for example, related to epidemic spreading, cardiac arrhythmias, or even population collapse. In this perspective, we briefly review past research dedicated to critical slowing down indicators and associated tipping points, and we outline promising directions for future research.