This paper presents a two-level control strategy for bipedal walking mechanism that accounts for implicit control of push-off on the between-step control level and tracking of imposed holonomic constraints on kinematic variables via feedback control on within-step control level. The proposed control strategy was tested in a biologically inspired model with minimal set of segments that allows ev...

We describe an attracting piecewise rotation with two atoms with a self-similar structure of periodic domains on its attractor which resembles Sierpi nski's gasket. Besides its natural beauty, this example appears a return map in certain piecewise aane maps on the torus which have been studied by Adler, Kitchens, and Tresser, and by a number of other researchers advancing the theory of digital ...

This paper describes the chaos shift keying method based on the second derivative desynchronization error and provides its security analysis, especially against the attacks by power and return map analysis. Desynchronization chaos shift keying method (DECSK) uses methods to detect the correct bit by detecting the wrong bit. Various modifications are possible, here the method using sharp increas...

0. Introduction We consider (possibly infinite dimensional) Lie algebras over a fixed field k of characteristic zero. Let g be a Lie algebra, S = Sg and U = Ug the symmetric and universal enveloping algebras, and F ⊂ F ⊂ · · · ⊂ U the coalgebra filtration F := k + g + g + · · ·+ g. Recall that the Poincaré-Birkhoff-Witt isomorphism between S and the associated graded ring GFU is induced by the ...

This paper introduces a new no–equilibrium chaotic system that is constructed by adding a tiny perturbation to a simple chaotic flow having a line equilibrium. Dynamics of the proposed system are investigated through Lyapunov exponents, bifurcation diagram, Poincaré map and period–doubling route to chaos. A circuit realization is also represented. Moreover, two other new chaotic systems without...

This paper delineates a class of time-periodically perturved evolution equations in a Banach space whose associated Poincaré map contains a Smale horseshoe. This implies that such systems possess periodic orbits with arbitrarily high period. The method uses techniques originally due to Melnikov and applies to systems of the form ẋ = f0(x) + εf1(x, t), where ẋ = f0(x) is Hamiltonian and has a ho...

4 Phase analysis 5 4.1 Local Stability at The Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4.2 Global Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4.2.1 0 < ρ < 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4.2.2 1 < ρ < ρh . . . . . . . . . . . . . . . . . . . ...

Introduction and Review 2 1. Period domains and monodromy 4 2. Elliptic curves 8 3. Period mappings: an example 12 3.1. Asymptotics of the period map 14 4. Hodge structures of weight one 15 5. Hodge structures of weight two 18 6. Poincaré residues 20 7. Properties of the period mapping 24 8. The Jacobian ideal and the local Torelli theorem 25 9. The Horizontal Distribution Distance Decreasing P...

We propose a model-based reinforcement learning algorithm for biped walking in which the robot learns to appropriately place the swing leg. This decision is based on a learned model of the Poincaré map of the periodic walking pattern. The model maps from a state at a single support phase and foot placement to a state at the next single support phase. We applied this approach to both a simulated...

In this paper, a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further, to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or numerically, such as Poincaré map, Lyapunov exponents and Lyapunov dimension. Based on this flow, a new almost-Hamilton chaotic system with very high Lyapunov ...