Bifurcation Analysis of a Four-Dimensional System of Two Symmetric Coupled Nonlinear Oscillators with Clearance

The research gradually highlights vibration and dynamical analysis of symmetric coupled nonlinear oscillators model with clearance. The aim of this paper is the bifurcation analysis of the symmetric coupled nonlinear oscillators modeled by a four-dimensional nonsmooth system. The approximate solution of this system is obtained with aid of averaging method and Krylov-Bogoliubov (KB) transformation presented by new notations of matrices. The bifurcation function is derived to investigate its dynamic behaviour by singularity theory. The results obtained provide guidance for the nonlinear vibration of symmetric coupled nonlinear oscillators model with clearance.

Averaging method and two-sided bounded solutions on the axis of systems with impulsive effects at non-fixed times

The averaging method, originally offered by Krylov and Bogolyubov for ordinary differential equations, is one of the most widespread and effective methods for the analysis of nonlinear dynamical systems. Further, the averaging method was developed and applied for investigating of various problems. Impulsive systems of differential equations supply as mathematical models of objects that, during their evolution, they are subjected to the action of short-term forces. Many researches have been devoted to non-fixed impulse problems. For these problems, the existence, stability, and other asymptotic properties of solutions were studied and boundary value problems for impulsive systems were considered. Questions of the existence of periodic and almost periodic solutions to impulsive systems also were examined. In this paper, the averaging method is used to study the existence of two-sided solutions bounding on the axis of impulse systems of differential equations with non-fixed times. It is shown that a one-sided, bounding, asymptotically stable solution to the averaged system generates a two-sided solution to the exact system. The closeness of the corresponding solutions of the exact and averaged systems both on finite and infinite time intervals is substantiated by the first and second theorems of N.N. Bogolyubov.

Relativistic Dynamical Stability Criterion of Multiplanet Systems with a Distant Companion

Multiplanetary systems are prevalent in our Galaxy. The long-term stability of such systems may be disrupted if a distant inclined companion excites the eccentricity and inclination of the inner planets via the eccentric Kozai–Lidov mechanism. However, the star–planet and the planet–planet interactions can help stabilize the system. In this work, we extend the previous stability criterion that only considered the companion–planet and planet–planet interactions by also accounting for short-range forces or effects, specifically, relativistic precession induced by the host star. A general analytical stability criterion is developed for planetary systems with N inner planets and a relatively distant inclined perturber by comparing precession rates of relevant dynamical effects. Furthermore, we demonstrate as examples that in systems with two and three inner planets, the analytical criterion is consistent with numerical simulations using a combination of Gauss’s averaging method and direct N-body integration. Finally, the criterion is applied to observed systems, constraining the orbital parameter space of a possible undiscovered companion. This new stability criterion extends the parameter space in which an inclined companion of multiplanet systems can inhabit.

A Novel Contractor Selection Technique Using the Extended PROMETHEE II Method

Selecting suitable contractors directly influences product quality, corporate profits, and even sustainable development. The selection problem of contractors is, therefore, a critical issue for the sustainable development of an enterprise. However, traditional contractor selection techniques are unable to handle information regarding the relative importance of criteria or handle nonexistent or missing data in the assessment process of contractor selection. In order to effectively address this problem, this study proposes a new contractor selection technique that integrates the concept of soft set and the PROMETHEE II method to select suitable contractors. Three numerical examples are applied to prove the correctness and effectiveness of the proposed technique. This study also compares the simulation results achieved using the proposed method with those achieved using the traditional weighted arithmetic averaging method and the data envelopment analysis (DEA) technique. The simulation results show that the proposed method is a more general contractor selection technique for handling incomplete information than the traditional weighted arithmetic averaging method and the DEA method.

On the Oscillation of Solutions of Differential Equations with Neutral Term

In this work, new criteria for the oscillatory behavior of even-order delay differential equations with neutral term are established by comparison technique, Riccati transformation and integral averaging method. The presented results essentially extend and simplify known conditions in the literature. To prove the validity of our results, we give some examples.

Concept of Flocks Fragmentation and Averaging Method for the Application of Electrocoagulation in Process for Coke Oven Wastewater Treatment

The main objective of the article is to develop the concept of flock fragmentation and the averaging method for the application of electrocoagulation in the process of treating wastewater from coke ovens. The designed solution was part of an innovative system for the coke oven wastewater treatment process. The system is dedicated to removing the hazardous elements and compounds from wastewater from leaching ashes in municipal waste incineration plants. The design of the process and its automatization was based on a quantitative simulation method. The balance equations of mass, energy, and momentum of transport, complemented by the kinetics of the related reaction, are used during the calculation of the process. The main result achieved is a practical solution—the reactor’s scheme, classified due to a patent procedure in the Polish Patent Office.