<p style='text-indent:20px;'>In this paper, we consider a piezoelectric beams system with magnetic effects and delay term. We study its long-time behavior through the associated dynamical system. prove that is gradient asymptotically smooth, which as consequence, implies existence of global attractor, characterized unstable manifold set stationary solutions. also get quasi-stability by es...

Dynamics with a threshold input-output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements induced by the interaction. Through global diffusive coupling, novel states are found to be generated that are not the original attractor of single-element thresho...

We delineate a mathematical model for the dynamics of the spread of ectoparasites and the diseases transmitted by them. We present how the dynamics of the system depends on the three reproduction numbers belonging to three of the four possible equilibria and give a complete characterization of the structure of the global attractor in each possible case depending on the reproduction numbers. Key...