The existence of a heteroclinic bifurcation for the Michaelis–Menten-type ratiodependent predator-prey system is rigorously established. Limit cycles related to the heteroclinic bifurcation are also discussed. It is shown that the heteroclinic bifurcation is characterized by the collision of a stable limit cycle with the origin, and the bifurcation triggers a catastrophic shift from the state o...

We are interested in understanding the mechanisms behind and the character of the sway motion of healthy human subjects during quiet standing. We assume that a human body can be modelled as a single-link inverted pendulum, and the balance is achieved using linear feedback control. Using these assumptions, we derive a switched model which we then investigate. Stable periodic motions (limit cycle...

We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting exam...

Answering a question of Adrian Bondy [4], we prove that every strong digraph has a spanning strong subgraph with at most n + 2α − 2 arcs, where α is the size of a maximum stable set of D. Such a spanning subgraph can be found in polynomial time. An infinite family of oriented graphs for which this bound is sharp was given by Odile Favaron [3]. A direct corollary of our result is that there exis...

This study reports the immobilization of a new lipase isolated from oleaginous seeds of Pachira aquatica, using beads of calcium alginate (Alg) and poly(vinyl alcohol) (PVA). We evaluated the morphology, number of cycles of reuse, optimum temperature, and temperature stability of both immobilization methods compared to the free enzyme. The immobilized enzymes were more stable than the free enzy...

The focus of studies in the field of passive walking has often been on straight walking, while less attention has been paid to the field of turning motions. In this paper, the passive motions of a finite width rimless wheel as the simplest 3D model of passive biped walkers was investigated with a focus on turning motions. For this purpose, the hybrid model of the system consisting of continuous...

We study topological dynamics on unshielded planar continua with weak expanding properties at cycles for which we prove that the absence of wandering continua implies backward stability. Then we deduce from this that a polynomial f with a locally connected Julia set is backward stable outside any neighborhood of its attracting and neutral cycles. For a conformal measure μ this easily implies th...

Based on Rabinovich system, a 4D Rabinovich system is generalized to study hidden attractors, multiple limit cycles and boundedness of motion. In the sense of coexisting attractors, the remarkable finding is that the proposed system has hidden hyperchaotic attractors around a unique stable equilibrium. To understand the complex dynamics of the system, some basic properties, such as Lyapunov exp...

Let G be a graph with order n, and let k be an integer with 1 ≤ k ≤ n/3. In this article, we show that if σ2(G) ≥ n+ k− 1, then for any stable set S ⊆ V (G) with |S| = k, there exists a 2-factor with precisely k cycles C1, . . . , Ck such that |V (Ci) ∩ S| = 1 for all 1 ≤ i ≤ k and at most one of the cycles Ci has length strictly greater than three. The lower bound on σ2 is best possible.

Anode materials of nanostructured silicon have been prepared by physical vapor deposition and characterized using electrochemical methods. The electrodes were prepared in thin-film form as nanocrystalline particles ~12 nm mean diameter! and as continuous amorphous thin films ~100 nm thick!. The nanocrystalline silicon exhibited specific capacities of around 1100 mAh/g with a 50% capacity retent...