In this paper, hidden bifurcation routes to multiscroll chaotic attractors generated by saturated function series are explored. The method to nd such hidden bifurcation routes (HBR) depending upon two parameters is similar to the method introduced by Menacer, et al. (2016) for Chua multiscroll attractors. These HBR are characterized by the maximal range extension (MARE) of their attractors and coding the appearance order of the scrolls under the control of the two parameters. Moreover, these HDR have interesting symmetries with respect to the two parameters. The novelty that this article introduces, is firstly the paradigm of MARE and the formula giving their approximate value depending upon parameters p and q, which is linked to the size of the scrolls; secondly the coding of the HBR which is dened for the first time including the basic cell; and thirdly unearthing the symmetries of these routes, allowing to obtain their coding without any numerical computation.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

This paper introduces a novel chaotic system that features a line of equilibrium and a unique multi-spiral chaotic sea. Unlike classical conservative chaotic systems, this model cannot directly exhibit a zero divergence but its conservative property can be confirmed by the zero sum of Lyapunov exponents. In addition, the system is shown to support the generation of coexisting nested hidden tori under specific parameter and initial conditions. The detailed dynamic analysis is presented using bifurcation diagrams, Lyapunov exponent, and phase portrait. The corresponding analog circuit is designed with circuitry simulations results to verify the theoretical predictions and numerical simulations.

The convective motions of rotating fluids under G-Jitter effect are of interest in industrial applications based on mechanisms of defining the structure verses quality of the material, homogeneity verses inhomogeneity of heating, laminar verses turbulent waves, oscillating verses non-oscillating vortices, and few others. This manuscript presents fractal modeling of G-Jitter effect for thermal analysis of rotating fluid via fractional differential as well as integral approach. The fractal–fractionalized mathematical model is proposed in terms of system of evolutionary differential equations that describes chaotic phenomenon under sensitivity of imposed initial conditions. The numerical simulations have also been generated by means of fractal–fractional differential as well as integral approach based on non-singularity and non-locality. The heat transfer effect of gravity modulation and rotation on amplitudes have also been investigated in phase portraits with dynamical chaotic behaviors. Our results suggest that high-frequency modulated fluid layer is unstable and low-frequency-modulated fluid layer is stable during chaotic convection.

This study introduces a novel robotic control paradigm, “chaos redirection,” which utilizes a single chaotic Hopfield Neural Network (HNN). We introduce “false attractors” synthetic trajectories created by applying controlled temporal shifts to the HNN’s state variables. This method allows a single chaotic source to be sculpted into distinct, task-specific behaviors for autonomous robots. We apply this framework to three applications: area cleaning, systematic search, and security patrol. Quantitative, statistically validated analysis demonstrates the successful generation of functionally distinct behaviors, including high-frequency, confined re-visitation for security patrols; maximized exploratory efficiency for search tasks; and high-entropy, non-repetitive paths for thorough cleaning. Our findings establish this as a robust and computationally efficient framework for applications requiring unpredictable, yet structured, behavior.

In this article, the behavior of hidden bifurcation in a two-dimensional (2D) scroll via saturated function series controlled by the coefficient harmonic linearization method is presented. A saturated function series approach for chaos generation. The systematic saturated function series methodicalness improved here can make multi-scroll and grid scroll chaotic attractors from a 3D linear autonomous system with a plain saturated function series supervisor. We have used a hidden bifurcation method in grid scroll., where the method of hidden bifurcation presented by Menacer, et al. in (2016) for Chua multi-scroll attractors. This additional parameter, which is absent from the initial problem, is perfectly adapted to unfold the structure of the multispiral chaotic attractor. The novelty of this article is twofold: first, the saturated function series model for hidden bifurcation in a 2 – D scroll; and second, the control of hidden bifurcation behavior by the value of the harmonic coefficient k 3 {k}_{3} .