This paper introduces a new four-dimensional hyperchaotic financial system on the basis of an established three-dimensional nonlinear financial system and a dynamic model by adding a controller term to consider the effect of control on the system. In terms of the proposed financial system, the sufficient conditions for nonexistence of chaotic and hyperchaotic behaviors are derived theoretically. Then, the solutions of equilibria are obtained. For each equilibrium, its stability and existence of Hopf bifurcation are validated. Based on corresponding first Lyapunov coefficient of each equilibrium, the analytical proof of the existence of periodic solutions is given. The ultimate bound and positively invariant set for the financial system are obtained and estimated. There exists a stable periodic solution obtained near the unstable equilibrium point. Finally, the dynamic behaviors of the new system are explored from theoretical analysis by using the bifurcation diagrams and phase portraits. Moreover, the hyperchaotic financial system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integrations and its real contribution to engineering.

Piezoelectric materials possess excellent electromechanical coupling characteristics, which are functional and suitable in structural vibration control. This study investigates the active control of free and forced vibration for piezoelectric-integrated functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate using the finite element method (FEM). Based on the first-order shear deformation theory (FSDT), the governing equations of the motion of a piezoelectric-integrated FG-CNTRC plate are derived by Hamilton’s principle. The convergence and accuracy of the numerical method is verified through the results of natural frequencies. The influences of CNT volume fraction, CNT distribution type, piezoelectric layer thickness-to-plate thickness ratio, and boundary condition on the natural frequencies are investigated. A constant gain velocity feedback algorithm is used to achieve the dynamic response control of the piezoelectric-integrated FG-CNTRC plate. In addition, the effects of dynamic load, feedback control gain, and boundary condition on the dynamic response of the plate are studied. Numerical results indicate that active control is promising for practical applications in civil and mechanical engineering.

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