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In this paper, we consider controlling and anti-controlling Hopf bifurcations in discrete maps using feedback controller of polynomial functions. It is shown that such a polynomial feedback controller is easy to be implemented, which not only preserves the system s equilibrium solutions, but also keeps the dimension of the system unchanged. Examples are(More)
The stability, instability, and bifurcation behaviour of a nonlinear autonomous system in the vicinity of a compound critical point is studied in detail. The critical point is characterized by two distinct pairs of pure imaginary eigenvalues of the Jacobian, and the system is described by two independent parameters. The analysis is based on a generalized(More)
A self-excited system involving a van der Pol-type damping and a hysteretic damper representing restoring force is investigated in this paper. The influence of external force on the dynamic behavior of the hysteretic system is analyzed in detail. Numerical simulations show that, under an external force, the original hysteretic system can exhibit the(More)
In this paper, the problem of implications of time delay feedback control of a two-dimensional supersonic lifting surface on the flutter boundary and on its character, that is, benign or catastrophic, is addressed. In this context, the structural and aerodynamic nonlinearities are included in the aeroelastic governing equations. The model and the associated(More)
A procedure, we call it generalized competitive mode (GCM), is proposed to estimate the parameter regimes of chaos in nonlinear systems by implementing a mathematical version of mode competition. The idea is that for a system to be chaotic there must exist at least two GCMs in the system. The Lorenz system and a thin plate in flow-induced vibrations system(More)
In this paper, we study complex dynamical behaviour in biological systems due to multiple limit cycles bifurcation. We use simple epidemic and predator-prey models to show exact routes to new types of bistability, that is, bistability between equilibrium and periodic oscillation, and bistability between two oscillations, which may more realistically(More)
In this paper, a new method is proposed for controlling bifurcations of nonlinear dynamical systems. This approach employs the idea used in deriving the transition variety sets of bifurcations with constraints to find the stability region of equilibrium points in parameter space. With this method, one can design, via a feedback control, appropriate(More)
In this paper, we consider bifurcation of small limit cycles from Hopf-type singular points in Z5-equivariant planar vector fields of order 5. We apply normal form theory and the technique of solving coupled multivariate polynomial equations to prove that the maximal number of small limit cycles that such vector fields can have is 25. In addition, we show(More)
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