This article presents a project that aims at constructing a biologically inspired amphibious snake-like robot. The robot is designed to be capable of anguilliform swimming like sea-snakes and lampreys in water and lateral undulatory locomotion like a snake on ground. Both the structure and the controller of the robot are inspired by elongate vertebrates. In particular, the locomotion of the rob...

We expose a grave drawback hidden in the standard model of n¯ n transitions in a medium. Correcting it, one improves a limit on the free-space n¯ n oscillation time τ n¯ n by 31 orders of magnitude.

We study the periodic solutions of the generalized Abel equation x′ = a1A1(t)x 1+a2A2(t)x 2+a3A3(t)x n3 , where n1, n2, n3 > 1 are distinct integers, a1, a2, a3 ∈ R, and A1, A2, A3 are 2π-periodic analytic functions such that A1(t) sin t,A2(t) cos t, A3(t) sin t cos t are πperiodic positive even functions. When (n3−n1)(n3−n2) < 0 we prove that the equation has no nontrivial (different from zero...

Toral translations are the simplest dynamical systems. In this talk I will discuss the fluctuations of the number of visits of an orbit of a toral translation to a given set. In particular we discuss how the fluctuations depend on the geometry of the set.

A concept of phase asymptotic semiflow is defined. It is shown that any Lagrange stable orbit at which the semiflow is phase asymptotic limits to a stable periodic orbit. A Lagrange stable solution of a C 1 differential equation is considered. When the second compound of the variational equation with respect to this solution is uniformly asymptotically stable and the omega limit set contains no...

The phenomenon of time-periodic evolution of spatial chaos is investigated in the frames of oneand two-dimensional complex Ginzburg-Landau equations. It is found that there exists a region of the parameters in which disordered spatial distribution of the field behaves periodically in time; the boundaries of this region are determined. The transition to the regime of spatiotemporal chaos is inve...

We consider three examples of weekly perturbed centers which do not have geometrical equivalence: a linear center, a degenerate center and a non-hamiltonian center. In each case the number and amplitude of the limit cycles emerging from the period annulus are calculated following the same strategy: we reduce of all of them to locally equivalent perturbed integrable systems of the form: dH(x, y)...

It is well-known that a suitably designed unpowered mechanical biped robot can \walk" down an inclined plane with a steady periodic gait. The energy required to maintain the motion comes from the conversion of the biped's grav-itational potential energy as it descends. Investigation of such passive natural motions may potentially lead us to strategies useful for controlling active walking machi...

In this paper, we study a class of quasi-symmetric seventh degree system. By making two appropriate transformations of system (3) and calculating general focal values carefully, we obtain the conditions that the infinity and the elementary focus (− 2 , 0) become centers at the same time.Moreover, 12 limit cycles including 6 small limit cycles from the elementary focus and 6 large limit cycles f...