Generalized model of interacting dark energy and dark matter: Phase portrait analysis for evolving universe

The main aim of this work is to give a suitable explanation of present accelerating universe through an acceptable interactive dynamical cosmological model. A three-fluid cosmological model is introduced in the background of Friedmann–Lemaître–Robertson-Walker asymptotically flat spacetime. This model consists of interactive dark matter and dark energy with baryonic matter, taken as perfect fluid, satisfying barotropic equation of state. We consider dust as the candidate of dark matter. A scalar field [Formula: see text] represents dark energy with potential [Formula: see text]. Einstein’s field equations are utilized to construct a three-dimensional interactive autonomous system by choosing suitable interaction between dark energy and dark matter. We take the interaction kernel as [Formula: see text], where [Formula: see text] indicates the density of dark energy, [Formula: see text] is the interacting constant and [Formula: see text] is Hubble parameter. In order to explain the stability of this system, we obtain some suitable critical points. We analyze stability of obtained critical points to show the different phases of universe and cosmological implications. Surprisingly, we find some stable critical points which represent late-time dark energy-dominated era when a model parameter [Formula: see text] is equal to [Formula: see text]. We introduce a two-dimensional interactive autonomous system and after phase portrait analysis of it, we get several stable points which represent dark energy-dominated era and late-time cosmic acceleration simultaneously. Here, we also demonstrate the variation in interaction at vicinity of phantom barrier [Formula: see text]. From our work, we can also predict the future phase evolution of the universe.

Nonlinear signal processing, spectral, and fractal based stridor auscultation: A machine learning approach

The work reported in the paper analyses the adventitious stridor breath sound (ST) and the normal bronchial breath sound (BR) using spectral, fractal, and nonlinear signal processing methods. The sixty breath sound signals are subjected to power spectral density (PSD) and wavelet analyses to understand the temporal evolution of the frequency components. The energy envelope of the PSD plot of ST shows three peaks labelled as A (256 Hz), B (369 Hz), and C (540 Hz), of which A alone is present in BR at 265 Hz. The appearance of B and C in the PSD plot of ST is due to the obstructions in the trachea and upper airways caused by lesions. The phase portrait analysis of the time series data of ST and BR gives information about the randomness and the sample entropy of the dynamical system. The study reveals that the fractal dimension and sample entropy values are higher for BR, which may be due to the musical ordered behaviour of ST. The machine learning techniques based on the features extracted from the PSD data and phase portrait parameters offer good predictability, besides the classification of BR and ST, and thereby revealing its potential in pulmonary auscultation.

Fast-Slow Coupling Dynamics Behavior of the van der Pol-Rayleigh System

In this paper, the dynamic behavior of the van der Pol-Rayleigh system is studied by using the fast–slow analysis method and the transformation phase portrait method. Firstly, the stability and bifurcation behavior of the equilibrium point of the system are analyzed. We find that the system has no fold bifurcation, but has Hopf bifurcation. By calculating the first Lyapunov coefficient, the bifurcation direction and stability of the Hopf bifurcation are obtained. Moreover, the bifurcation diagram of the system with respect to the external excitation is drawn. Then, the fast subsystem is simulated numerically and analyzed with or without external excitation. Finally, the vibration behavior and its generation mechanism of the system in different modes are analyzed. The vibration mode of the system is affected by both the fast and slow varying processes. The mechanisms of different modes of vibration of the system are revealed by the transformation phase portrait method, because the system trajectory will encounter different types of attractors in the fast subsystem.

Acoustic and phase portrait analysis of leading-edge roughness element on laminar separation bubbles at low Reynolds number flow

Since laminar separation bubbles are neutrally shaped on the suction side of full-span wings in low Reynolds number flows, a roughness element can be used to improve the performance of micro aerial vehicles. The purpose of this article was to investigate the leading-edge roughness element’s effect and its location on upstream of the laminar separation bubble from phase portrait point of view. Therefore, passive control might have an acoustic side effect, especially when the bubble might burst and increase noise. Consequently, the effect of the leading-edge roughness element features on the bubble’s behavior is considered on the acoustic pressure field and the vortices behind the NASA-LS0417 cross-section. The consequences express that the distribution of roughness in the appropriate dimensions and location could contribute to increasing the performance of the airfoil and the interaction of vortices produced by roughness elements with shear layers on the suction side has increased the sound frequency in the relevant sound pressure level (SPL). The results have demonstrated that vortex shedding frequency was increased in the presence of roughness compared to the smooth airfoil. Also, more complexity of the phase portrait circuits was found, retrieved from velocity gradient limitation. Likewise, the highest SPL is related to the state where the separation bubble phenomenon is on the surface versus placing roughness elements on the leading edge leads to a negative amount of SPL.