Dynamical behaviour and stability control of new hyperchaotic finance system
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Date
2024
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Faculty of Science, University of Kelaniya Sri Lanka
Abstract
In economic activities, chaos is undesirable as it can lead to an economic crisis and should be addressed promptly. In chaotic situations, it is desirable to control the chaotic orbits to a stable state, a periodic orbit, or to synchronize the chaotic system. Various control and synchronization methods have been developed and tested to achieve this. The new hyperchaotic finance system proposed by Yu, Cai, and Li in 2012 is a non-linear coupled system of four differential equations. Linear control method, speed feedback method, recursive backstepping control method, backstepping sliding mode control method, and adaptive control strategies have already been applied to synchronize and stabilize new hyperchaotic finance system. However, most of these methods lack one or more desired features of a control method, such as simplicity, feasibility, and efficiency. Therefore, in this work, we investigate the feasibility of two different control methods for addressing the chaos of the new hyperchaotic finance system. Firstly, the dynamical behaviours of the new hyperchaotic finance system were examined using waveforms, phase portraits, equilibrium points, Lyapunov exponents, and bifurcation diagrams. The results indicate that this system exhibits intricate features and evolves into chaotic, hyperchaotic and periodic phenomena based on parameter variations. Secondly, we propose and implement the two control methods for the new hyperchaotic finance system, namely the active control method and the active backstepping technique, which possess the desirable properties of a control method. The validity and effectiveness of the two control methods are illustrated using numerical simulations. The Active Backstepping technique was utilized to stabilize the unstable motion of trajectories globally at the origin. The computer simulation results have been compared with the existing speed feedback control method, showing that the designed controllers regulate the new hyperchaotic finance system to the origin at t = 5s and the speed feedback controller at t = 30s. The comparison shows that the performance of the proposed control method is better than the speed feedback control method for stabilizing of the hyperchaotic finance system as it converges faster. The active and backstepping control techniques have been utilized to synchronize the two new hyperchaotic finance systems. The numerical simulations have proven that over time, the Slave hyperchaotic finance system can replicate the chaotic dynamics of the Master hyperchaotic finance system after activating the designed controllers. Additionally, the Slave system synchronized with the Master System by eliminating the error between the state variables of the two systems. Finally, it was concluded that the designed controllers are suitable for controlling the new hyperchaotic finance system to track any trajectory that is a smooth function of time, as well as for stabilizing at any position effectively.
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Keywords
Active backstepping method, Active control method, New hyperchaotic finance system
Citation
Nimansa K. H. K.; Perera B. B. U. P. (2024), Dynamical behaviour and stability control of new hyperchaotic finance system, Proceedings of the International Conference on Applied and Pure Sciences (ICAPS 2024-Kelaniya) Volume 4, Faculty of Science, University of Kelaniya Sri Lanka. Page 103