Identifying the governing equations of a nonlinear dynamical system is key to both understanding physical features and constructing an accurate model dynamics that generalizes well beyond available data. We propose machine learning framework for discovering these using only partial observations, combining encoder state reconstruction with sparse symbolic model. Our tests show this method can su...

Many engineering and natural systems are dynamical systems. For example a pendulum is a dynamical system. l mg 2 Figure 1. Simple pendulum. State The state of the dynamical system specifies it conditions. For a pendulum in the absence of external excitation shown in the figure, the angle and the angular velocity uniquely define the state of the dynamical system. Plots of the state variables aga...

Generalized thermoelastic models have been developed with the aim of eliminating the contradiction in the infinite velocity of heat propagation inherent in the classical dynamical coupled thermoelasticity theory. In these generalized models, the basic equations include thermal relaxation times and they are of hyperbolic type. Furthermore, Tzou established the dual-phase-lag heat conduction theo...

Abstract

This paper presents a novel method for analyzing slowly modulated oscillator behavior. This occurs, for example, when the values of some oscillator components are changed through an external signal that varies much slower than the oscillation time constant. Applications exhibiting this type of behavior are phase-locked loops (PLLs) or frequency-modulation-based transmitters. Both examples invol...

This paper presents a MPC (Model Predictive Control) algorithm for MEMS vibratory gyroscopes based on force-balancing control strategy. In the proposed MPC method, using a set of orthonormal basis functions named Laguerre functions, a new prediction and optimization technique is designed. To enhance the capability of proposed MPC method for tracking time-varying reference trajectories, first a ...

In this paper we give a complete description of the Fredholm spectrum of the linearized 3D Euler equation in terms of the dynamical spectrum of the cocycle governing the evolution of shortwave perturbations. The argument is based on the pseudo differential representation of the Euler group and an application of an abstract isomorphism theorem for operator C∗-algebras. We further show that for a...

The evolution of cosmic string networks is an interesting dynamical problem. The equations governing these networks are classical and fully specified, but the length scale at which cosmic string loops form has been uncertain to tens of orders of magnitude. Numerical simulations are limited in the range of length and time scales they can reach, while analytic methods have been limited by the non...

We propose a new technique for the numerical reconstruction of nonlin-ear delay diierential equations from time series by applying the method of optimal transformations, a concept of multiple nonlinear regression analysis. By constructing a generalized correlation function, this method allows for testing time series for delay-induced dynamics. Also, the delay times and the governing diierential...