We present a framework for feature extraction and mode decomposition of spatiotemporal data generated by ergodic dynamical systems. Unlike feature extraction techniques based on kernel operators, our approach is to construct feature maps using eigenfunctions of the Koopman group of unitary operators governing the dynamical evolution of observables and probability measures. We compute the eigenv...

In this article, bending, buckling, and free vibration of viscoelastic sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core on viscoelastic foundation are presented using a new first order shear deformation theory. According to this theory, the number of unknown’s parameters and governing equations are reduced and also the using of shear correct...

Impact responses of rectangular composite plates with embedded shape memory alloy (SMA) wires are investigated in the present research. The plate is assumed to be placed in a thermal environment; so that in contrast to the available researches in the field, the shape memory and ferroelasticity effects have to be considered also in addition to the superelasticity. The governing equations are der...

We study the Maxwell–Bloch equations governing a two-level laser in a ring cavity. For Class A lasers, these equations have two widely separated time scales and form a singularly perturbed, semilinear hyperbolic system with two distinct characteristics. We extend Fenichel’s geometric singular perturbation theory [N. Fenichel, J. Differential Equations, 31 (1979), pp. 53–98] to the Maxwell–Bloch...

Chua’s circuit (see Fig. 1) is one of the simplest physical models that has been widely investigated by mathematical, numerical and experimental methods. One of the main attractions of Chua’s circuit is that it can be easily built with less than a dozen standard circuit components, and has often been referred to as the poor man’s chaos generator. A mathematical analysis of the global unfolding ...

The nonlinear dynamical system modeling the immobilized enzyme kinetics with Michaelis-Menten mechanism for an irreversible reaction without external mass transfer resistance is considered. Laplace transform homotopy perturbation method is used to obtain the approximate solution of the governing nonlinear differential equation, which consists in determining the series solution convergent to the...

The Koopman operator is a linear but infinite-dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system and is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. In this manuscript, we present a data-driven method for approximating the leading eigenvalues, eigenfunctions, and modes of the Ko...

Nacre, commonly known as mother-of-pearl, is a remarkable biomineral that in red abalone consists of layers of 400-nm thick aragonite crystalline tablets confined by organic matrix sheets, with the (001) crystal axes of the aragonite tablets oriented to within ±12 from the normal to the layer planes. Recent experiments demonstrate that this orientational order develops over a distance of tens o...

Usually mathematicians use Hodgkin-Huxley model or FitzHug-Nagumo model to simulate action potentials of skeletal muscle fibers. These models are electrically excitable, but skeletal muscle fibers are stimulated chemically. To investigate skeletal muscle fibers we use a model with six ordinary differential equations. This dynamical system is sensitive to initial value of some variables so it is...