The analysis of dynamic instability and vibration motions of a pinned beam with transverse magnetic fields and thermal loads

Parametric instability of a cantilever beam with magnetic field and periodic axial load

Strongly Nonlinear Subharmonic Resonance and Chaotic Motion of Axially Moving Thin Plate in Magnetic Field

Active H∞ control of the vibration of an axially moving cantilever beam by magnetic force

To study the dynamics of quasi-periodic bifurcations, we consider a system of two nonlinearly coupled oscillators using averaging, continuation and numerical bifurcation techniques. This relatively simple system displays considerable complexity. Assuming the internal resonance to be 1:2, we find a 2π-periodic solution which undergoes a supercritical Neimark–Sacker bifurcation, yielding a stable torus. Choosing a route in parameter space, we show by numerical bifurcation techniques how the torus gets destroyed by dynamical and topological changes in the involved manifolds (Krauskopf and Osinga in J Comput Phys 146:404–419, 1998). The 1:6 resonance turns out to be prominent in parameter space, and we detected a cascade of period doublings within the corresponding resonance tongue yielding a strange attractor. The phenomena agree with the Ruelle–Takens (Commun. Math. Phys. 20:167–192, 1971, Commun. Math. Phys. 23:343–344, 1971) scenario leading to strange attractors. Other periodic regimes are present in this system, and there is interesting evidence that two different regimes interact with each other, yielding yet another type of strange attractor. In this context, certain π-periodic solutions emerge that are studied by continuation following the Poincare–Lindstedt method using Mathieu functions; when the implicit function theorem breaks down, the analysis is supplemented by numerical bifurcation techniques.

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Bifurcations of quasi-periodic dynamics: torus breakdown

Dynamic stability and bifurcation of an alternating load and magnetic field excited magnetoelastic beam

Secondary bifurcations of two non-linearly coupled oscillators

Structural oscillations of non-inner resonance and inner resonance induced by vortex shedding are studied using the method of multiple scales under different conditions. It is shown that the vortex-excited system exhibits complicated dynamic behaviours such as frequency-locked, subharmonic, superharmonic and quasiperiodic oscillations.

Subharmonic. superharmonic and quasiperiodic oscillations induced by vortices

The Leslie–Gower model, a kind of predator–prey model with weak Allee effect, is studied in this paper. The existence and stability of non-negative equilibria are first discussed. Then, we investigate several bifurcation phenomena undergoing positive equilibria, such as saddle-node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation, etc. Some possible dynamical behaviors of this model are illustrated by numerical simulation. The bifurcation diagrams for the cases of codimensions 2 and 3 are given respectively. The coexistence of a periodic cycle and a homoclinic cycle, and two limit cycles enclosing an unstable equilibrium are also proved. This appears to be the first study of the Leslie–Gower model including the influence of weak Allee effect on prey.

K.L. Huang

Papers

Dynamic stability and bifurcation of an alternating load and magnetic field excited magnetoelastic beam

Secondary bifurcations of two non-linearly coupled oscillators

Subharmonic. superharmonic and quasiperiodic oscillations induced by vortices

Bifurcation Analysis of a Modified Leslie-Gower Predator-Prey System