Numerical continuation methods for large-scale dissipative dynamical systems

Numerical algorithms for stationary statistical properties of dissipative dynamical systems

It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. The main concern of this manuscript is numerical methods for dissipative chaotic infinite dimensional dynamical systems that are able to capture the stationary statistical properties of the underlying dynamical systems. We first survey results on temporal and spatial approximations that enjoy the...

Thermodynamics and Large-scale Non- Linear Dynamical Systems: a Vector Dissipative Systems Approach

Recent technological demands have required the analysis and control design of increasingly complex, large-scale nonlinear dynamical systems. In analyzing these largescale systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solution properties of the large-scale system are then deduced from the solution properties of the individual subsystems ...

Dissipative Dynamical Systems

Continuation of Bifurcations of Periodic Orbits for Large-Scale Systems

A methodology to track bifurcations of periodic orbits in large-scale dissipative systems depending on two parameters is presented. It is based on the application of iterative Newton–Krylov techniques to extended systems. To evaluate the action of the Jacobian it is necessary to integrate variational equations up to second order. It is shown that this is possible by integrating systems of dimen...

A partition-based algorithm for clustering large-scale software systems

Clustering techniques are used to extract the structure of software for understanding, maintaining, and refactoring. In the literature, most of the proposed approaches for software clustering are divided into hierarchical algorithms and search-based techniques. In the former, clustering is a process of merging (splitting) similar (non-similar) clusters. These techniques suffered from the drawba...