Dynamical study of a novel 4D hyperchaotic system: An integer and fractional order analysis

In this article, a new nonlinear four-dimensional hyperchaotic model is presented. The dynamical aspects of the complex system are analyzed covering equilibrium points, linear stability, dissipation, bifurcations, Lyapunov exponent, phase portraits, Poincare mapping, attractor projection, sensitivity and time series analysis. To analyze hidden attractors, the proposed system is investigated through nonlocal operator in Caputo sense. The existence of solution of the system in fractional sense is studied by fixed point theory. The stability of fractional order system is demonstrated via Matignon stability criteria. The fractional order system is numerically studied via newly developed numerical method which is based on Newton polynomial interpolation. The evolution of the attractors are depicted with different fractional orders. For few fractional orders, some hidden strange chaotic attractors are observed through graphs. Theoretical and numerical studies demonstrate that this model has complex dynamics with some stimulating physical characteristics. To verify and validate the results, we implement Field Programmable Analog Arrays (FPAA).(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

In this article, a new nonlinear four-dimensional hyperchaotic model is presented and analyzed extensively. The research covers various aspects of the complex system, including equilibrium points, stability, dissipation, bifurcations, Lyapunov exponent, phase portraits, Poincare mapping, attractor projection, sensitivity, and time series analysis. The study also explores hidden attractors and investigates the system in the fractional sense. Theoretical and numerical studies reveal the complex dynamics and stimulating physical characteristics of the model.