Vol. 9, No. 3 (2020): Regular Issue

This paper investigates the behaviour of frictional bolted supports that are example of boundary conditions exhibiting nonlinear stick-slip phenomena and act as bilinear hysteretic systems which is modelled here by Jenkins frictional element. An Euler-Bernoulli beam containing bolted supports under white noise excitation is considered. The dependence of equivalent damping and variance of the response amplitude to joint stiffness, sliding threshold and input intensity are identified and optimum sliding threshold is obtained to have minimum overall variance of system response. Further, the Monte-Carlo simulation is developed to verify the results and shown that when the Jenkins stiffness is big enough, the Linearization technique and Monte-Carlo simulation are in good agreement.

In this article we present a model that describes the emerging dynamic scenario of infection with the human T-cell lymphotropic virus (HTLV-I). In this model we incorporate the phase of latency in the infection of the CD4+ lymphocytes, the immune response mediated by CD8+ T lymphocytes and the possible appearance of adult T-cell leukemia (ATL). The proposed model is a six-dimensional, non-linear system of ordinary differential equations that describes the dynamic interactions among different cell types. Several types of biological implications are discussed.

The present theoretical investigation is dealt with stability of the model system characterizing the formation of atherosclerotic plaques emerging from the interactions between several cellular species in the media of blood stream and its surrounding vascular region. The biochemical processes behind the formation of atherosclerotic plaque involve the interactions between several cellular species like low density lipoprotein, free radicals, chemoattractants, monocytes, macrophages, T-cells, smooth muscle cells, foam cells and collagen. Taking all these complex events into account, an appropriate mathematical model depicting the onset of atherosclerotic plaques in the arterial lumen is constructed through the system of ten nonlinear ordinary differential equations (ODEs) for the concentrations of most pertinent components of the atherosclerotic constraints. Besides conducting an in-depth study of the model including several sub-models for their stability criteria, special emphasis is also paid on a reduced model system having adequate relevance to the present system following Quasi Steady State Approximation (QSSA) theory. Both the local and the global stability together with the bifurcation analysis for the reduced model system are carried out analytically. Results of numerical simulation based on the model parameter values reveal the time-series representations for the concentrations of all the interacting species, the local and the global stability and bifurcations with respect to some parameters of significance for the reduced model system under study. The complex features of several subsystems are also examined through several phase portraits in order to explore the clinical implications of atherosclerotic lesion in the arterial lumen. The model validation is also performed through comparison of the present results with those of previous ones [1].

In this paper, we consider the initial boundary value problem for the three species cooperating model under various boundary conditions in which the solution may blow up in finite time. Explicit lower bound for blow up time is being obtained by using techniques based on Sobolev type and first order differential inequalities.

This paper deals with predator-prey eco-epidemiological model where an infectious disease among fish population is non-linearly transmitted in a reserve area. Then the disease is transmitted indirectly to the predator population during their feeding process. At the time of harvesting, both the susceptible and the infected prey population are harvested. When the nonlinear disease transmission and the inhibition effect on the dynamical behavior of the prey are measured, the number of infected individuals increases. The model in this study is analyzed in term of boundedness, and local and global stability under certain conditions and Hopf bifurcation. For the determine of optimal conditions, we have compared the theoretical results with numerical results for different sets of parameters.

Some of the biological species like tiger, deer and monkeys in Sundarbans, the largest mangrove forest in the world have been driven to extinction due to several external forces such as illegal poaching, over exploitation, predation, environmental pollution and mismanagement of habitat.This paper deals with a ratio-dependent predator-prey model with prey refuge and illegal harvesting of both species.The boundedness of solution, feasibility of interior equilibria have been determined. Optimal control technique has been applied to investigate anti-poaching patrol strategy for controlling the threat in the predator prey system facing in Sundarbans. The system is also ex- amined so that the better control strategy is achieved. Moreover, the control strategy is obtained on the effect of variation of prey refuge.

Based on the nonlocal strain gradient theory, a Euler-Bernoulli nanobeam model subjected to the compressive axial force and resting on the Winkler-Pasternak layer is developed to study buckling and free nonlinear vibration problems. Critical buckling force and nonlinear frequency of simply supported nanobeam are analytically derived. Comparison of obtained analytical solutions with published and numerical ones shows accuracy of the present solutions. Effects of the scale factor, the aspect ratio, the Winkler parameter and the Pasternak parameter on the critical buckling force ratio and the vibration response of the nanobeam are studied in this work.

In the present research work, the Timoshenko beam element theory has been used to develop the finite element model of the turbocharger rotor system. The nonlinear fluid film forces generated in floating ring bearings have been derived. A new MATLAB code has been constructed using Newmark-β numerical integration scheme along with Newton-Raphson method to solve the equations of motion of the system. The orbital plots, Poincaremaps, and time response plots are obtained at different nodes, for various speeds to study the nonlinear dynamic behavior of floating ring bearings and turbocharger rotor system.

This paper deals with a nonlinear integro-differential equation of fractional order aϵ(0,1) with nonlocal conditions involving fractional derivative in the Caputo sense. Under a new approach and minimal assumptions on the function f , we prove the existence, uniqueness, estimates on solutions and continuous dependence of the solutions. The used techniques in analysis rely on fractional calculus, Banach contraction mapping principle, and Pachpatte's inequality. At the end, some numerical examples to justify our results are illustrated.

The wavelet analysis is a fairly new approach to the study of various systems, especially for financial markets. Wavelet transform is the decomposition of a one-dimensional signal based on a soliton-like function (wavelet) by its stretching (compression) and displacement along the time axis. In a period of a market-driven global economy, when financial crises are significant sources of destabilization of not the economy only, anticipation and minimization of losses from global financial crises are very important. The study of the currency market is one of the pressing problems of the modern economy, which in its turn addresses the mathematical tools. The purpose of the work is to determine the main regularities in the numerical series of the Ukraine hryvnia (UAH) against the US dollar and the Russian ruble (RUR) to the US dollar (USD).

In this paper, we study the oscillatory behavior of damped second-order mixed nonlinear differential equation with variable delay under impulse effects. By using Riccati transformation technique, integral averaging method and some inequalities, we obtain sufficient conditions for oscillation of all solutions. Finally, two examples are presented to illustrate the theoretical results.

In this article, we investigate a class of neutral stochastic integrodifferential equations with impulsive effects. The results are obtained by using the new integral inequalities, the attracting and quasi-invariant sets combined with theories of resolvent operators. Moreover, exponential stability of the mild solution is established with sufficient conditions. An example is provided to illustrate the results of this work.