We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The...

We consider the displayed phenomena in the semi-passive dynamic walking of a torso-driven biped robot under the OGY control method as it descends inclined surfaces. The desired torso angle is the accessible control parameter. Analysis of the controlled steady semi-passive gaits are carried out mainly by means of bifurcations diagrams and Poincaré sections as the slope parameter varies. Based on...

We prove two kinds of fibering theorems for maps X → P , where X and P are Poincaré spaces. The special case of P = S yields a Poincaré duality analogue of the fibering theorem of Browder and Levine.

This paper presents basic theoretical results for partial constant return maps (PCRMs) from controlled manifold piecewise linear chaotic circuits. Applying the instantaneous state setting method to the circuit, the chaotic attractor is changed into various superstable periodic orbits corresponding to the PCRM. Using an efficient algorithm, an important example of the PCRM can be analyzed almost...

We present an algorithm to compute one-dimensional stable and unstable manifolds of saddle periodic orbits in a Poincaré section. The computation is set up as a boundary value problem by restricting the beginning and end points of orbit segments to the section. Starting from the periodic orbit itself, we use collocation routines from AUTO to continue the solutions of the boundary value problem ...

Systems with impulse effects form a special class of hybrid systems that consist of an ordinary, time-invariant differential equation (ODE), a co-dimension one switching surface, and a re-initialization rule. The exponential stability of a periodic orbit in a C-nonlinear system with impulse effects can be studied by linearizing the Poincaré return map around a fixed point and evaluating its eig...