Nonlinear behavior of a novel chaotic jerk system: antimonotonicity, crises, and multiple coexisting attractors

A Novel Compound-Coupled Hyperchaotic Map for Image Encryption

Considering a nonlinear dynamic oscillator, a high Lyapunov exponent indicates a high degree of randomness useful in many applications, including cryptography. Most existing oscillators yield very low Lyapunov exponents. The proposed work presents a general strategy to derive an n-D hyperchaotic map with a high Lyapunov exponent. A 2D case study was analyzed using some well-known nonlinear dynamic metrics including phase portraits, bifurcation diagrams, finite time Lyapunov exponents, and dimension. These metrics indicated that the state of the novel map was more scattered in the phase plane than in the case of some traditional maps. Consequently, the novel map could produce output sequences with a high degree of randomness. Another important observation was that the first and second Lyapunov exponents of the proposed 2D map were both positive for the whole parameter space. Consequently, the attractors of the map could be classified as hyperchaotic attractors. Finally, these hyperchaotic sequences were exploited for image encryption/decryption. Various validation metrics were exploited to illustrate the security of the presented methodology against cryptanalysts. Comparative analysis indicated the superiority of the proposed encryption/decryption protocol over some recent state-of-the-art methods.

Multistability analysis and nonlinear vibration for generator set in series hybrid electric vehicle through electromechanical coupling

The non-linear analysis of undesired vibrations observed on hybrid electric vehicle (HEV) powertrains is hardly developed in the literature. In this paper, a mathematical modeling of the vibrations observed at the level of the electromechanical coupling between the internal combustion engine and the generator in the series architecture of HEVs, named (SHEVs), is established using the Lagrangian theory. The stability and instability motions of this SHEV are perfectly detailed using amplitude-frequency response curves. An analysis of the electromagnetic torque amplitude of the new SHEV demonstrates the presence of multistability with the coexistence of two or three different types of attractors. In addition, this new SHEV model has other dynamic regimes of chaotic and periodic oscillations. Coexisting bifurcations with parallel branches, hysteresis, and period-doubling are also discovered. A unique contribution of this work is the abundance and complicated dynamical behaviors found in such types of systems compared with some rare cases previously reported on HEV powertrain models. The simulation results obtained using non-linear analysis tools sufficiently demonstrate that the objectives of this paper are achieved.

A Multistable Chaotic Jerk System with Coexisting and Hidden Attractors: Dynamical and Complexity Analysis, FPGA-Based Realization, and Chaos Stabilization Using a Robust Controller

In the present work, a new nonequilibrium four-dimensional chaotic jerk system is presented. The proposed system includes only one constant term and has coexisting and hidden attractors. Firstly, the dynamical behavior of the system is investigated using bifurcation diagrams and Lyapunov exponents. It is illustrated that this system either possesses symmetric equilibrium points or does not possess an equilibrium. Rich dynamics are found by varying system parameters. It is shown that the system enters chaos through experiencing a cascade of period doublings, and the existence of chaos is verified. Then, coexisting and hidden chaotic attractors are observed, and basin attraction is plotted. Moreover, using the multiscale C0 algorithm, the complexity of the system is investigated, and a broad area of high complexity is displayed in the parameter planes. In addition, the chaotic behavior of the system is studied by field-programmable gate array implementation. A novel methodology to discretize, simulate, and implement the proposed system is presented, and the successful implementation of the proposed system on FPGA is verified through the simulation outcome. Finally, a robust sliding mode controller is designed to suppress the chaotic behavior of the system. To deal with unexpected disturbances and uncertainties, a disturbance observer is developed along with the designed controller. To show the successful performance of the designed control scheme, numerical simulations are also presented.