Based on the concept of double central extension from categorical Galois theory, we study a notion of commutator which is defined relative to a Birkhoff subcategory B of a semi-abelian category A. This commutator characterises Janelidze and Kelly’s B-central extensions; when the subcategoryB is determined by the abelian objects inA, it coincides with Huq’s commutator; and when the category A is...

It is well known that in an o-minimal hybrid system the continuous and discrete components can be separated, and therefore the problem of finite bisimulation reduces to the same problem for a transition system associated with a continuous dynamical system. It was recently proved by several authors that under certain natural assumptions such finite bisimulation exists. In the paper we consider o...

In this paper, the dynamics of multicellular chopper are considered. The model is described by a continuous time three--dimensional autonomous system. Some basic dynamical properties such as Poincar'e mapping, power spectrum and chaotic behaviors are studied. Analysis results show that this system has complex dynamics with some interesting characteristics.

This paper presents the effect of preload on nonlinear dynamic behavior of a rigid rotor supported by two-lobe aerodynamic noncircular journal bearing. A finite element method is employed to solve the Reynolds equation in static and dynamical states and the dynamical equations are solved using Runge-Kutta method. To analyze the behavior of the rotor center in the horizontal and vertical directi...

Our recent work [28] proposes the DeGroot-Friedkin dynamical model for the analysis4of social influence networks. This dynamical model describes the evolution of self-appraisals in a5group of individuals forming opinions in a sequence of issues. Under a strong connectivity assumption,6the model predicts the existence and semi-global attractivity of equilibrium configurat...

An autonomous Caputo fractional differential equation of order α ∈ (0,1) in a finite dimensional space whose vector field satisfies global Lipschitz condition is shown to generate semi-dynamical system the function $\mathfrak {C}$ continuous functions with topology uniform convergence on compact subsets. This contrasts recent result Cong and Tuan (J. Integral Equ. Appl.: 29, 585–608, 2017), whi...