Robust attracting heteroclinic cycles have been found in many models of dynamics with symmetries. In all previous examples, robust heteroclinic cycles appear between a number of symmetry broken equilibria. In this paper we examine the first example where there are robust attracting heteroclinic cycles that include the origin, ie a point with maximal symmetry. The example we study is for vector ...

Complex combinatorial optimization can be used to design network systems having desired dynamics and that are robust against structural perturbations. Here genetic networks exhibiting limit-cycle oscillations with prescribed periods and, furthermore, that are robust against the deletion of links and nodes or the application of noise are constructed. Large ensembles of robust genetic clocks with...

Recent efforts to develop large-scale brain and neurocognitive architectures have paid relatively little attention to the use of self-organizing maps (SOMs). Part of the reason for this is that most conventional SOMs use a static encoding representation: each input pattern or sequence is effectively represented as a fixed point activation pattern in the map layer, something that is inconsistent...

In this paper we seek to quantify and explicitly optimize the robustness of a control system for a robot walking on terrain with uncertain geometry. Geometric perturbations to the terrain enter the equations of motion through a relocation of the hybrid event “guards” which trigger an impact event; these perturbations can have a large effect on the stability of the robot and do not fit into the ...

In this paper, a synthetic jet actuators (SJA)-based nonlinear robust controller is developed, which is capable of completely suppressing limit cycle oscillations (LCO) in UAV systems with parametric uncertainty in the SJA dynamics and unmodeled external disturbances. Specifically, the control law compensates for uncertainty in an input gain matrix, which results from the unknown airflow dynami...

We analyze the Higgs sector in the Next-to-Minimal Supersymmetric Standard Model, emphasizing the possibility of a light CP-odd scalar (axion) in the spectrum. We compute the coupling of the Standard-Model-like Higgs boson to a pair of axions, and show that it can be large enough to modify the Higgs branching fractions, with a significant impact on the Higgs searches. We delineate the range of ...

The problem of limit cycles for Kolmogorov model is interesting and significant both in theory and applications. Our work is concerned with limit cycles bifurcations problem for a class of quartic Kolmogorov model with two positive singular points (i.e. (1, 2) and (2, 1)). The investigated model is symmetrical with regard to y = x. We show that each one of points (1, 2) and (2, 1) can bifurcate...