Vol. 8, No. 3 (2019): Regular Issue

This paper describes a methodology for designing an adaptive tracking controller of an atomic force microscope to estimate a surface profile of a sample. A microbeam of the atomic force microscope is modeled as an Euler-Bernoulli beam with single mode considered. A tip-sample interaction force used here is a piecewise function described by the attractive van der Waals force and the repulsive Derjaguin-Muller-Toporov force which can represent the indentation made by a tip of the microbeam into the sample surface. The adaptive-tracking controllers for both regions are designed based on adaptive control Lyapunov functions. With the driving and measured signals, the controlled acceleration is generated and superimposed onto the harmonic excitation and the estimated surface profile is obtained. If the tip of the microbeam taps harder on the sample surface, the more estimation error is obtained. To reduce the estimated surface-profile error, the regression model needs more higher-order terms to approximate the repulsive Derjaguin-Muller-Toporov force.

The dynamics of the classical Lorenz system is well studied in 1963 by E. N. Lorenz. Later on, there have been an extensive studies on the classical Lorenz system with the complex variables and the discrete time Lorenz system with real variables. To the best of knowledge of the author, so far there is no study on discrete time Lorenz system in complex variables. In this article, an attempt has been made to observe and understand the discrete dynamics of the Lorenz system with complex variables. This study compares the discrete dynamics of the Lorenz system with complex variables to that of the classical Lorenz system involving real and complex variables.

In this paper, we investigate a stochastic two species prey-predator system with prey refuge. The contribution of this paper is (a) To Propose a Lotka-Volterra stochastic model with prey refuge (b) Singular cases are very interesting and it is found that without the prey population, the predators died with probability one while without predator population prey population fallen between 0 & ∞. Impact of refuge term is also observed. (c) The Radon-Nikodym Derivative is derived for the proposed model (d) Asymptomatic analysis and moment estimation for the proposed model is also carried out. As a possible application of proposed stochastic model, Keoladeo National Park, India is considered.

The purpose of this manuscript is to study the approximate controllability of stochastic fractional impulsive neutral integro-differential equations with state dependent delay and Poisson jumps by using fixed point techniques. By the help of stochastic analysis theory and fractional calculus, we have derived the controllability results. Finally, an example is given to illustrate the obtained abstract result.

In this article we present the existence, uniqueness and stability of mild solutions for impulsive stochastic functional integro differential equations with non-Lipschitz condition. The mild solution is obtained by using a resolvent operator in a different sense and the results are proved by using the method of successive approximation and Bihari’s inequality.

The major aim of this paper is to study the dynamical behaviour of a prey-predator system where the prey exhibits herd behaviour. Positivity, boundedness, some extinction criteria, stability of equilibrium points are represented with some global results. Numerical computations are discussed to illustrate the analytical findings. The biological implications of analytical and numerical findings are represented. This work also has a direct bearing to the possibilities of developing conditions for ecological balance in nature and by elaborate study and analysis, it throws enough light on the scope of further work in this field.

In this paper, by combining full state hybrid projective synchronisation (FSHPS) and inverse full state hybrid projective synchronisation (IFSHPS), we generalize the idea of hybrid chaos synchronization in discrete-time. Based on stability theory of linear discrete-time systems and Lyapunov stability theory, new approaches are proposed to investigate the new type of hybrid synchronization between chaotic maps of different dimensions. Several numerical examples have highlighted the effectiveness of the novel approaches developed herein.

The goal of this paper is to study a fractional output stabilization problem: the stabilization of the state fractional spatial derivative of complex purely imaginary order i α with α ∈]0,1[, for bilinear distributed systems. Firstly, we develop sufficient conditions for exponential, strong and weak fractional output stabilization for the considered system, also, we offer some examples illustrating the obtained results. Moreover, we characterise the stabilizing control which minimizes an appropriate cost. Finally, an illustrating example with numerical simulations is given.

In this study a novel method, namely multiple exponential function scheme is performed for nonlinear evolution equations. Based on first order auxiliary equations, one-, two-, and three-wave solutions can be established by using computerized symbolic computations. For illustrating the effectiveness of this approach, we apply the method to solve (3+1) dimensional classical Jimbo-Miwa and it’s extended (3+1) dimensional forms. In addition, we determine dispersion relation and phase shift for each of the models.

The paper analyses frequency synchronization characteristics of two Van der Pol oscillators coupled by a NEMS varactor. Equations of motion are derived by taking into account the voltage nonlinearity of the NEMS varactor. The synchronization conditions are obtained in the form of coupled algebraic equations between synchronization frequency, amplitude ratio and phase difference. The synchronization frequency in phase quadrature is controlled by amplitude ratio of the coupled oscillators. A comparative analysis of synchronization characteristics is also presented for coupling by a fixed value capacitor. It is found that NEMS coupled system is tunable over an order of magnitude greater frequency range under identical conditions for quadrature tolerance. The NEMS varactor coupling does not require a master-slave like condition for attaining phase quadrature. The analyses for phase sensitivity and linear stability are performed. The stable synchronization occurs for the amplitude ratio being more than 0.7. The paper illustrates that NEMS capacitive coupling of Van der Pol oscillators facilitates amplitude ratio as controlling parameter for synchronization, and results in enhanced tunability and quadrature accuracy.

In the present paper, we extend our attempt of modeling the closed loop control of glucose concentration level by considering three time delays for the proper functioning of artificial pancreas. Several time delays exist in the glucose - insulin regulatory system, the time delays which we are considering in the present study are delay in insulin secretion, delay in inhibition in hepatic glucose production stimulated by insulin and delay in time taken by insulin to reach interstitial compartment to lower glucose level (i.e. glucose utilization delay or insulin action delay). None of the time delay is negligible. Our analytical and numerical results shows that periodic and sustained oscillations of glucose and insulin concentration exists for type 1 diabetic people and delay in insulin secretion may be one of the major possible reason behind the occurrence of ultradian oscillations. Range of all three time delays have been quantified from the simulation of present model, which may be proved very useful in better designing and improved functioning of artificial pancreas.

In this paper, an application of fractional-order PIλ controller is given as an alternative to solve some control problems that can arise. It aims to apply the analytical tuning procedure to control the heat flow systems. This system, modeled by first-order system involving time delay, is one with open loop characteristic equations are fractional order quasi-polynomials. Using the proposed method, the entire stability region of PI λ controllers is obtained and visualized in the plane (Kp,Ki, λ ). The simulation was carried out on thermal systems and the results demonstrate the effectiveness of the proposed type of controllers and the tuning rule.