Vol. 9, No. 2 (2020): Regular Issue

This paper investigates different type of synchronization between fractional-order (chaotic, hyperchaotic) systems and integer-order (chaotic, hyperchaotic) systems. Based on the idea of the decomposition of the controller in the response system in two sub-controllers and the stability theory of the linear integer-order system, we design the effective controller to realize the synchronization, Antisynchronization, function projective synchronization, inverse function projective synchronization between fractional-order and integer-order systems. Finally, the fractional-order L¨u’s system and the Lorenz system of integer order are used to demonstrate the effectiveness of the proposed method with numerical simulation.

In this paper the solar radiation data available in some stations across Nigeria are analysed to understand the underlying dynamics of the natural time series for the purpose of good prediction and modelling of solar power generation in the country. The solar radiation data observed over a period of two years by National Space Research and Development Agency (NASRDA) from five different stations in the tropics are studied using recurrence based methods. The underlying dynamics of the hourly solar radiation data are investigated using recurrence plot (RP) and recurrence quantification analysis (RQA). From the RQA results for each month of the two years, it is observed for all the five stations that solar radiation exhibits high (low) chaoticity during the wet (dry) season due to nonlinear interaction of the solar radiation with high (low) atmospheric water vapour contents coupled with strong (weak) West Africa monsoonal effect during the wet (dry) season. Sudden transitions into or out of a ‘wet’ or ‘dry’ season which are caused mainly by external effect such as intertropical discontinuity (ITD) on solar radiation data are identified. The results show that recurrence techniques are able to identify areas and periods for which the harvest of solar energy for power generation is optimum (high predictability) and poor (low predictability) in the study areas.

This paper presents a practical implementation for a new formula of nonlinear PID (NPID) control. The purpose of the controller is to accurately trace a preselected position reference of one stage servomechanism system. The possibility of developing a transfer function model for experimental setup is elusive because of the lack of system data. So, the identified model has been developed via gathering experimental input/output data. The performance of the enhanced nonlinear PID (NPID) controller had been investigated by comparing it with linear PID controller. The harmony search (HS) tuning system had built to determine the optimum parameters for each control technique based on an effective objective function. The experimental and simulation results proved that the enhanced nonlinear PID (NPID) controller has better performance and more robust compared to linear PID controller. Both the simulation and the experimental results are identical significantly.

In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynamical model equations is important in understanding of evolution process and reduce uncertainty. However, often used numerical methods are unable to do it on large time segments. In this article, the author considers the modern numerical method and algorithm for constructing solutions of chaotic systems on the example of tumor growth model. Also a modification of Benettin’s algorithm presents for calculation of Lyapunov exponents.

In the present paper, the combined effect of magnetic field and nonuniform shape of the surface on squeeze film characteristics is investigated. The non-uniform squeeze film thickness is calculated using Lagrange interpolation technique. Numerical integration procedure is used to obtain the solution for pressure, load carrying capacity. The effects of field parameters on squeeze film characteristics are discussed and are presented graphically. It is observed that externally applied magnetic field and non-uniform shape of the bearing surface enhance the squeeze film lubrication.

Unemployment problems have become the most immense concerns all over the world. This issue is significantly an alarming concern in Bangladesh as well. This paper deals with a nonlinear mathematical model of unemployment which describes the situation of unemployment, employment and vacancies. The system of nonlinear differential equations has been developed and analyzed with two policies of government. In this study, we describe and analyze the modified model and check the stability of equilibrium points of the model. We also discuss the characteristics of states at equilibrium point for various parameters. Specially, we establish a project of five years toreduce the unemployment problems. We also simulate our model in the present of two optimal controls of unemployment model using optimal control technique.

In this paper we investigate the dynamical systems generated by gonosomal evolution operator of sex linked inheritance depending on parameters. Mainly we study dynamical systems of a hemophilia which is biological group of disorders connected with genes that diminish the body’s ability to control blood clotting or coagulation that is used to stop bleeding when a blood vessel is broken. For the gonosomal operator we discrebe all forms and give explicitly the types of fixed points. Moreover we study limit points of the trajectories of the corresponding dynamical system.

The classical theory of stereo-mechanical impact is widely used in practice. This theory is based on the law of conservation of energy and the law of conservation of momentum. The main purpose of this study is to determine the optimal mass ratios and velocity ratios of colliding bodies, which are the basis of the impact mechanism. The solution of this problem is necessary for calculating the maximum energy efficiency of the impact system. In this paper, we obtain a coupling equation for the energy and momentum conservation laws, as well as for the Newtonian restitution coefficient equation for a simultaneous central stereo-mechanical impact of bodies.

In this work, a secure communication scheme based on the synchronization of non-identical hyperchaotic systems is considered. Using hyperchaotic Lorenz and L ü as prototype oscillators, a secure communication scheme based on synchronization of different hyperchaotic systems with unknown parameters is presented. The communication scheme consists of a transmitter, which comprises the hyperchaotic carrier and modulator, and a receiver, which comprises the hyperchaotic response and a demodulator. Appropriate controllers and parameter update laws are designed to achieve synchronization between the hyperchaotic drive and hyperchaotic response systems and achieve the estimate of unknown parameters simultaneously. The message signal is recovered by the identified parameter and the corresponding demodulation method. Numerical simulations were performed to show the validity and feasibility of the designed secure communication scheme.

In this paper we have studied Left and Right ventricular hypertrophy of heart from ECGs using fractional calculus. An ECG is a rough or unreachable curve which is continuous everywhere but nondifferentiable at some points or all points where classical calculus fails. Our purpose of this paper is to find left and right fractional derivatives at those non-differentiable points and then predict LVH and RVH by calculating the phase transition values (absolute difference of left and right fractional derivatives). Our investigation shows that for LVH patients the phase transition values at the non-differentiable points of V1, V2, V5 and V6 leads are higher than those for normal ECG. For RVH ECG the phase transition values at S are smaller than those of R in V1 leads which are just opposite to the case of normal ECGs. Fractal dimension and Hurst Exponents of V1, V2, V5 and V6 leads of the ECGs have been calculated for both problematic and normal ECGs. All such measures may help doctors to diagnose LVH and RVH from ECG more accurately than the technique they use.

In this work, nonlinear dynamics and parametric excitation of piezoelectric micro beam subjected a combination of DC and AC voltages is investigated for micro biological sensor applications. The governing differential equation of the motion is derived by the Hamiltonian principle and then by using the Galerkin approach, this partial differential equation (PDE) is simplified into an ordinary differential equation (ODE) in terms of forced damped Mathieu equation with cubic nonlinearity. A perturbation technique, i.e. multiple time scales approach is used for investigation of superharmonic resonances of orders 1/2 and 1/3 and obtaining of the modulation equations in the amplitude and phase. Numerical results of different parameters effects on the piezoelectric micro beam behavior are presented graphically.

In this paper, we consider a diffusive predator-prey system with modified Holling-Tanner functional response under homogeneous Neumann boundary condition . Dynamics of the system is very sensitive to the variation of the initial conditions. We determine stability and dynamical behaviors of the equilibrium of this system. The dynamical behaviors consist of Andronov-Hopf bifurcation, limit cycles and Bogdanov-Takens bifurcations. Numerical simulation results are given to support our theoretical results.