Based upon a novel paradigm of the galaxy formation under UV background, the evolutionary bifurcation of pregalactic clouds is confronted with observations on elliptical and spiral galaxies. The theory predicts that the dichotomy between the dissipational and dissipationless galaxy formation stems from the degree of self-shielding from the UV background radiation. This is demonstrated on a bifu...

Transitions from normal-mode to local-mode states in the two bending oscillations of acetylene observed in spectroscopic studies, as well as the existence of localized vibrational states in vinylidene above the isomerization barrier to acetylene, are examined by constructing continuation/ bifurcation diagrams of periodic orbits on a global potential-energy surface. The principal families of per...

We give closed expressions for classical symmetric solutions of boundary value problems for the one-dimensional Willmore equation. Navier as well as Dirichlet boundary conditions are considered. In the first case, one has existence of precisely two solutions for boundary data below a suitable threshold, precisely one solution on the threshold and no solution beyond the threshold. This effect re...

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous gr...

Brushless DC Motor (BLDCM) has high reliability, long service life, which, however, is a typical multivariable, strong coupled complicated nonlinear system. There peacefully coexist complex dynamical behaviors, such as limit cycles and chaotic attractors, coexists peacefully. Therefore, this paper proposes the BLDCM system, to explore these dynamics, we compute and simulate the bifurcation diag...

We investigate the dynamics of a droplet on a planar substrate as the droplet volume changes dynamically due to liquid being pumped in or out through a pore. We adopt a diffuse-interface formulation which is appropriately modified to account for a localized inflow-outflow boundary condition (the pore) at the bottom of the droplet, hence allowing to dynamically control its volume, as the droplet...

The Korteweg de Vries (KdV) equation with small dispersion is a model for the formation and propagation of dispersive shock waves in one dimension. Dispersive shock waves in KdV are characterized by the appearance of zones of rapid modulated oscillations in the solution of the Cauchy problem with smooth initial data. The modulation in time and space of the amplitudes, the frequencies and the wa...

Anti-control of chaos of single time-scale brushless DC motors is studied in this paper. In order to analyse a variety of periodic and chaotic phenomena, we employ several numerical techniques such as phase portraits, bifurcation diagrams and Lyapunov exponents. Anti-control of chaos can be achieved by adding an external constant term or an external periodic term.

Traditionally, terms together with Sweedler notation are used to express computations in (generalized) bialgebras. Here, an algebra is a vector space equipped with an operation μ : ⊗→  and a bialgebra is an algebra  equipped with a co-operation δ :  →  ⊗ . The operation μ must be (bi)linear and satisfy some properties, for instance associativity and/or commutativity. Similarly, the co-op...

This paper deals with the dynamical behaviour of discrete Prey-Predator model with Holling type IV involving intra-specific competition. This model represents mathematically by nonlinear differential equations. The existence, uniqueness and boundedness solutions of this model were investigated. The locally asymptotic stability conditions of all possible equilibrium points were obtained. The sta...