Exploring attractors and basin dynamics in a new symmetric chaotic system: Analysis of complex synchronization patterns

Stability analysis is recognized as a critical aspect of the study of dynamical systems, which encompasses the identification of the system attractors, the assessment of their stability or instability, and the determination of the basins of attraction of these attractors. A notable characteristic of this novel system is its multiple attractors, which are attributed to varying initial conditions. A prominent feature of the system under investigation is its ability to exhibit multiple attractors, which arise from varying initial conditions. The dynamical properties of the proposed system have been thoroughly examined through the evaluation of Lyapunov exponents, bifurcation diagrams, and multi-stability. Various chaos detection tools, including the Poincaré map, power spectrum, and time series analysis, have been employed to identify chaotic behavior within the system. To enhance understanding and interpretation, comprehensive numerical and graphical illustrations have been provided. In addition, a novel overlapping technique has been employed to compute the common area between two data sets for the first time, offering a detailed qualitative examination of the complex dynamics of the system. The results obtained are novel and informative, contributing valuable information for future research and serving as a resource for ongoing studies in the field. • A comprehensive analysis of the generalized ( n + 1 ) -dimensional KP equation is conducted. • The phase space of the system is explored, revealing intricate chaotic structures, including spiral-shaped attractors. • Poincaré maps and power spectrum analysis are employed to detect periodic and chaotic behavior. • The research examines the basins of attraction, and overlapping solutions that highlight sensitivity to initial conditions.