Vol. 10, No. 1 (2021): Regular Issue

In this paper, a piezoelectric biomedical nanosensor (PBMNS) based on cylindrical nanoshell subjected to nonlinear electrostatic field and viscoelastic medium is introduced to investigate natural frequency and stability analysis of PBMNS conveying viscous bloodstream using the electro-elastic Gurtin--Murdoch surface/interface theory, Hamilton's principle and assumed mode method combined with Euler -- Lagrange. The effect of different parameters on natural frequencies and stability analysis of PBMNS is demonstrated. It is shown that bloodstream velocity due to motion of biomarkers has major unpredictable effects on natural frequency and critical fluid velocity of the system and one should precisely consider their effects.

The two-wheeled self-balancing human transporters (TW-SBHT) are being widely used in transportation nowadays owing to their advantages such as energy saving, environmental protection, simple structure, and flexible operation. The modelling and control of TW-SBHT have emerged as one of the trending research areas in the field of control system design of mobile robots. Being a complex and nonlinear system, the control problem of TW-SBHT is a challenging task and needs to be effectively tackled to achieve the control objectives of maintaining uniform speed and dynamic stability. Though linear control strategies for TW-SBHT have been already proposed in the literature, they cannot offer an effective control for large external disturbances. Therefore, in this work, a non-linear control i.e. State-Dependent Riccati Equation (SDRE) has been implemented for effective control of TW-SBHT and its performance is compared with the linear controls including Proportional-Integral-Derivative (PID) and Linear-Quadratic Regulator (LQR) techniques. Initially, the more accurate model of TW-SBHT has been derived by applying the suitable modifications in existing models. Then, the application of SDRE for control of TW-SBHT has been presented and its performance is compared with linear control strategies.

The problem of stability for nonlinear Hindmarsh-Rose (H-R) neuron model with event-triggered fuzzy Integral Sliding Mode Control (ISMC) design is investigated via Takagi-Sugeno (T-S) fuzzy systems. The Event-triggered Communication (ETC) scheme is introduced with a triggered condition of the sampling instant to determine whether the current sampled signal should be transmitted or not. {In order to send and receive the delay measurements for updating the control, the event triggered zero-order-holder (ZOH) is employed. Also, a note observer is designed for the estimation of system state and for the facilitation of the sliding surface design.} Then by analyzing the measured output and observer output, a novel law is presented. Further the stability criterion and the stabilization conditions are estimated based on Lyapunov-Krasovskii functional (LKF) to ensure the asymptotically stability for the considered system. Finally, a numerical example is presented to demonstrate the feasibility of the proposed design scheme.

Lie symmetry analysis is performed on a two-wave mode equation for the integrable Kadomtsev-Petviashvili (TKP) equation which describes the propagation of two different wave modes in the same direction simultaneously. The similarity reductions and an exact solution are computed. In addition to this, we derive the conservation laws for the underlying equation.

In this paper, we investigate the blow-up phenomena of non-negative solutions of a two-species Keller-Segel chemotaxis model with Lotka-Volterra competitive source terms. We estimate the lower bounds for the blow-up time of solutions of the model under the Neumann boundary conditions in a bounded domain $\Omega\subset\mathbb{R}^n, n\geq 1$. The first-order differential inequality technique is applied to determine the results in various space dimensions by using different auxiliary functions.

In this work, we use the alternative ($G'/G$)-expansion method, the sech method, the tanh method and the Painleve truncated approach to find solutions of the modified complex Ginzburg-Landau equation. We show that any mathematically acceptable solution is not necessarily physically suitable. Among the two types of obtained solutions, there is a category with null infinite branches, for which no direct numerical simulation can be carried out. This type of solutions is however mathematically well-grounded. The second type concerns new solutions with infinite non-zero branches. For this second type, direct numerical simulations are performed to show that they are physically valid.

Stability analysis of motions in a nonlinear periodically forced, nonlinear fractional time-delayed, is investigated. An enhanced perturbation method is developed to study the stability behavior for the nonlinear oscillator. The basic idea of the method is to apply the annihilator operator to construct a simplified equation freeness of the periodic force. This method makes the solution process for the forced problem much simpler. The resulting equation is valid for studying all types of possible resonance states. The outcome shows that this alteration method overcomes all shortcomings of the perturbation method and leads to the very high accuracy of the obtained solution.

In this paper we will investigate the dynamical behavior of the following rational difference equation $$x_{n+1}= \frac{\alpha + \beta x_{n} + \gamma x_{n-k}} {A +B x_{n} + C x_{n-k}},\quad n=0,1,... \tag{1}$$ where the parameters $\alpha, \beta, \gamma$ and A, B, C and the initial conditions $x_{-k},\dots,x_{-1},x_{0}$ are non-negative real numbers, and the denominator is nonzero. Our concentration here, is on the global stability, the periodic character, the analysis of semi-cycles and the invariant intervals of the positive solution of the above equation. It is worth mentioning that our difference equation is the general case of the rational equation which is studied by Kulenovic and Ladas in their monograph ( Dynamics of Second Order Rational Difference Equation with Open Problems and Conjectures, 2002 ).

In this paper, a numerical approach based on non-iterative integration method with a small deviating argument for nonlinear singularly perturbed two point boundary value problems is discussed. The technique of quasilinearization is used to linearize nonlinear singular perturbation problem into a set of linear singularly perturbed equations. The continuous problem is replaced by an approximate first order differential equation with a delay argument which is non-iterative and then the application of numerical integration method to achieve a recurrence relationship of three terms. To demonstrate the effectiveness the proposed method are experimented with nonlinear problems.

Low velocity impact response of GLARE (GLAss REinforced aluminium laminate) beam based on First Order Shear Deformation Theory is studied. The system energy is written and using Ritz method and generalized Lagrange equations, the motion equations are derived. Good agreement is achieved between this analytical method and available results. Results reveal that an increase of the impactor initial velocity causes increasing in the peak of contact force and peak of central beam deflection but decreasing contact time. Also, increasing of the impactor radius will enhances the peak of contact force and diminish peak of central beam deflection and contact time.

In this paper, we study the dynamics of small particle in the framework of the photo-gravitational restricted three body problem in the binary stellar masses. In this work, we consider three binary stellar systems Kepler-34, Kepler-35 and Kepler-16. The dynamics of the test particle in these three systems is studied in terms of the Poincar\'e surfaces of section method and the finite-time local Lyapunov exponents. We have computed full Lyapunov spectrum for this three binary systems. %Also maximum Lyapunov characteristic exponents (mLCEs) can be used as an indicator and a measure of the chaotic motion. We have obtained mLCEs with the help of numerical integration of equations of motion in the planar circular restricted three body problem considering both primaries as radiating. Poincar\'e surfaces of section for different values of radiation parameter are obtained and observed the corresponding changes accordingly. Also, we have obtained orbits and corresponding Poincar\'e surface of sections for all systems. Moreover, using actual values of radiation parameter, we have computed Poincar\'e surface of section for different values of Jacobi constant.

In this paper we are defining the fuzzy type of mixed delay differential equations. The necessity of studying the mixed delay differential equation in terms of fuzzy is that the single real valued solution can be ordered as the set of fuzzy valued solution. So it is very important in establishing the existence of solution for the fuzzy mixed type of delay differential equations using necessary theorems and lemmas. In addition we are also proving that the existing solution is unique.