Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations

The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e., 1：3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed. By numerical simulation, periodic vibration and quasi-periodic vibration responses of the Composite laminated piezoelectric plate are obtained.

DOUBLE HIGH ORDER S－BREAKING BIFURCATION POINTS AND THEIR NUMERICAL DETERMINATION

We consider double high order S-breaking bifurcation points of two-Parameter dependent nonlinear problems with Z_2×Z_2-symmetry. Because of the underlying symmetry we could propose some regular extended systems to determine double high order S-breaking bifurcation points. and we could also show that there exist two quadratic pitchfork bifurcation point paths passing through the point being considered.

Stochastic period-doubling bifurcation analysis of a Rssler system with a bounded random parameter

This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rossler system with an arch-like bounded random parameter. First, we transform the stochastic RSssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic RSssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rossler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rossler system.

Bifurcation and optimal control for an infectious disease model with the impact of information

A nonlinear infectious disease model with information-influenced vaccination behavior and contact patterns is proposed in this paper,and the impact of information related to disease prevalence on increasing vaccination coverage and reducing disease incidence during the outbreak is considered.First,we perform the analysis for the existence of equilibria and the stability properties of the proposed model.In particular,the geometric approach is used to obtain the sufficient condition which guarantees the global asymptotic stability of the unique endemic equilibrium Ee when the basic reproduction number Ro>1.Second,mathematical derivation combined with numerical simulation shows the existence of the double Hopf bifurcation around Ee.Third,based on the numerical results,it is shown that the information coverage and the average information delay may lead to more complex dynamical behaviors.Finally,the optimal control problem is established with information-infuenced vaccination and treatment as control variables.The corresponding optimal paths are obtained analytically by using Pontryagin's maximum principle,and the applicability and validity of virous intervention strategies for the proposed controls are presented by numerical experiments.

A SPLITTING ITERATION METHOD FOR DOUBLE X_0-BREAKING BIFURCATION POINTS

A splitting iteration method is proposed to compute double X0-breaking bifurcation points. The method will reduce the computational work and storage, it converges linearly with an adjustable speed. Numerical computation shows the effectiveness of splitting iteration method.