A singularly perturbed differential delay equation of the form ẋ(t) = −x(t)+ f (x(t − 1), λ) (1) exhibits slowly oscillating periodic solutions (SOPS) near the first period-doubling bifurcation point of the underlying map (obtained by setting = 0). For extremely small values of , these periodic solutions resemble square waves, which consist of sharp, O( ) transition layers connecting intervals ...

In the Trade Cycle, Hicks introduced the idea that endogenous fluctuations could be coupled with a growth process via nonlinear processes. To argue for this hypothesis, Hicks used a piecewise-linear model. This paper shows the need for a reinterpretation of Hicks’ contribution in the light of a more careful mathematical investigation. In particular, it will be shown that only one bound is neede...

Some classical tools have been used in the literature to study the positive solutions for twopoint boundary value problems of a coupled system of differential equations. These classical tools include some fixed point theorems in cones for completely continuous operators and Leray-Schauder fixed point theorem; for examples, see 1–3 and literatures therein. Recently, Schauder’s fixed point theore...

This paper mainly treats of the interconnections between the periodic Schur form and its associated periodical deflating subspaces. We establish some equivalent statements of the periodic Schur decomposition for regular periodic matrix pairs. Based on these equivalences, we define the eigenspaces for regular periodic matrix pairs, and point out the corresponding eigenvalues inherited from a giv...

Figure S1. Density of states (DOS) for the periodic structures of TiO2 anatase (a), phenyl-acac-TiO2 (b), and 3-acac-pyran-2-one-TiO2 (c), calculated at the extended Hückel level. The filled black lines in (b)-(c) are the projected DOS of the dye chromophores. The blue arrows point to the electronic states with a predominant contribution of HOMO, and the red arrows point to the electronic state...

This paper addresses the dynamic behaviour of a chemical oscillator arising from the series coupling of two Brusselators. Of particular interest is the study of the associated Hopf bifurcation and double-Hopf bifurcations. The motion of the oscillator may either be periodic (bifurcating from a Hopf-type critical point), or quasi-periodic (bifurcating from a compound critical point). Furthermore...

*Correspondence: [email protected] 1Theoretical and Computational Science Center (TaCS-Center), Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand 3Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan Full ...

A class of the linear impulsive periodic system with time-varying generating operators on Banach space is considered. By constructing the impulsive evolution operator, the existence of T0-periodic PC-mild solution for homogeneous linear impulsive periodic system with time-varying generating operators is reduced to the existence of fixed point for a suitable operator. Further the alternative res...

We describe simple one-dimensional models of passive (no energy input, no control), generally dissipative, vertical hopping and oneball juggling. The central observation is that internal passive system motions can conspire to eliminate collisions in these systems. For hopping, two point masses are connected by a spring and the lower mass has inelastic collisions with the ground. For juggling, a...