Many ecological systems exhibit multi-year cycles. In such systems, invasions have a complicated spatiotemporal structure. In particular, it is common for unstable steady states to exist as long-term transients behind the invasion front, a phenomenon known as dynamical stabilisation. We combine absolute stability theory and computation to predict how the width of the stabilised region depends o...

It is shown that in general for linear desynchronized systems there are no algebraic criteria of absolute stability.

Launched in April 1999, the Landsat-7 ETM+ instrument is in its fourth year of operation. The quality of the acquired calibrated imagery continues to be high, especially with respect to its three most important radiometric performance parameters: reflective band instrument stability to better than ±1%, reflective band absolute calibration to better than ±5%, and thermal band absolute calibratio...

In this paper we present a new approach to the Popov's Positivity Theorem and new statements and proofs of Absolute Stability Theorems. In the rst chapter we establish connexions between Riccati equations, Kalman-Yakubovitch-Popov systems and Luri e systems. We prove this results for stabilizable and antistabilizable solutions avoiding Youla's factorization. In the second chapter we state the A...

The problem of absolute stability is one of the oldest open problems in the theory of control. Even for the particular case of second-order systems a complete solution was presented only very recently. For third-order systems, the most general theoretical results were obtained by Barabanov. He derived an implicit characterization of the “most destabilizing” nonlinearity using a variational appr...

An analysis of the absolute stability for a general class of discrete-time recurrent neural networks (RNN's) is presented. A discrete-time model of RNN's is represented by a set of nonlinear difference equations. Some sufficient conditions for the absolute stability are derived using Ostrowski's theorem and the similarity transformation approach. For a given RNN model, these conditions are dete...

where γ is the observed environmental lapse rate, and Γ s and Γ d are the moistand dry-adiabatic lapse rates, respectively. Of particular interest here is state 5, dry absolutely unstable. Typically, this state exists in a shallow surface-based layer (usually < 100 mb deep) and results from an imbalance between the rate at which air adjacent to the ground is heated by conduction and the rate at...