The dynamical functional particle method (DFPM) is a method for solving equations by using a damped second order dynamical system. The dynamical system is solved by a symplectic method that is especially tailored for conservative systems. In this work we have extended DFPM to convex optimization problems with constraints. The method is tested on linear eigenvalue problems with normalization and...

The sensitive dependence of periodicity and chaos on parameters is investigated for three-dimensional nonlinear dynamical systems. Previous works have found that noninvertible low-dimensional maps present power-law exponents relating the uncertainty between periodicity and chaos to the precision on the system parameters. Furthermore, the values obtained for these exponents have been conjectured...

& Ersue, 1992) published a few years back on the subject of neurocontrol. The subject of neural networks for modeling and control of dynamical systems represents an important area of applications of artiÿcial neural networks that reemerged in 1980s. On the other hand, to control engineers , neurocontrol, or neural networks for controls, brings about some new and fresh ideas to the modeling and ...

The quantification of information flow between subspaces in ensemble predictions for complex dynamical systems is an important practical topic, for example, in weather prediction and climate change projections. While information transfer between dynamical system components is an established concept for nonlinear multivariate time series, the specific nature of the nonlinear dynamics generating ...

The paper proposes derivative-free nonlinear Kalman Filtering for MIMO nonlinear dynamical systems. The considered nonlinear filtering scheme which is based on differential flatness theory extends the class of systems to which Kalman Filtering can be applied without the need for calculation of Jacobian matrices. To deduce if a dynamical system is differentially flat, the following should be exa...

In this paper, we consider local and uniform invariance preserving steplength thresholds on a set when a discretization method is applied to a linear or nonlinear dynamical system. For the forward or backward Euler method, the existence of local and uniform invariance preserving steplength thresholds is proved when the invariant sets are polyhedra, ellipsoids, or Lorenz cones. Further, we also ...

We study a nonlinear transmission problem for a plate which consists of thermoelastic and isothermal parts. The problem generates a dynamical system in a suitable Hilbert space. Main result is the proof of asymptotic smoothness of this dynamical system and existence of a compact global attractor in special cases.

We introduce a novel control method for a delayed dynamical system exhibiting high-dimensional chaos. The control is based on a negative feedback loop with an adaptive filtering, consisting of a selective filter, centered at the frequency of the orbit to be stabilized, with the addition of a time derivative correction. The validity of the method is also discussed in the framework of a space-lik...

This paper focuses on the sensitivity analysis of coupled nonlinear dynamical systems, which under certain conditions exhibit the chaotic behavior. Sensitivity functions calculated via conventional methods of sensitivity analysis are inherently uninformative and inconclusive. The use of the pseudo-orbit shadowing property in dynamical systems allows calculating sensitivity functions correctly a...