Authors:P. G. Surkov Pages: 504 - 516 Abstract: The control-package method is applied to solve the problem of constructing guaranteed positional guidance for a linear control dynamical system with a delay under incomplete information about the initial state. The problem is solved for the case when the initial state is contained in a compact functional set. A solvability criterion and a method for the construction of a guidance program package are proposed. The proposed procedure is applied to a particular linear control system of delayed differential equations. PubDate: 2017-10-01 DOI: 10.1007/s10598-017-9377-y Issue No:Vol. 28, No. 4 (2017)

Authors:A. Khan; M. A. Bhat Pages: 517 - 530 Abstract: In this paper, a new nonlinear dynamical system has been studied which is obtained from the 3D chaotic system. The hyperchaotic analysis of the new system is checked in terms of dissipation, equilibrium points and their stability, Lyapunov exponent, time series, phase portraits, Poincaré section and bifurcation diagram. Furthermore, the adaptive projective synchronization technique is used to synchronize the novel hyperchaotic system. A brief theoretical analysis and simulation results are presented to prove the behavior of the novel hyperchaotic system. PubDate: 2017-10-01 DOI: 10.1007/s10598-017-9378-x Issue No:Vol. 28, No. 4 (2017)

Authors:V. P. Gor’kov; N. L. Grigorenko; A. E. Rumyantsev Pages: 531 - 549 Abstract: We construct a mathematical model of quadcopter flight and design a positional control that solves the terminal control problem in the presence of a disturbance parameter. The study relies on the results of [6–9] and provides sufficient existence conditions for a positional control that solves the control problem for a class of boundary conditions. PubDate: 2017-10-01 DOI: 10.1007/s10598-017-9379-9 Issue No:Vol. 28, No. 4 (2017)

Authors:B. V. Digas; V. L. Rozenberg Pages: 550 - 560 Abstract: One of the current topical problems is the prediction of climate change and mitigation of its consequences. All-sided analysis of ecological, economic, and social aspects of climate issues relies on interdisciplinary assessment models. This article adapts the MERGE optimization model to the current state of the world economy and introduces into the model a new component that implements a simplified procedure of “green” GDP calculation (“green” GDP, or GGDP, provides information about the efficiency of use of environmental resources). The objective of our numerical simulations is to tests the consequences of Russia’s hypothetical participation in the program for reducing greenhouse gas (GHG) emissions and to analyze the environmental indicators of Russia’s GDP. The input data are mainly provided by the project of scenario conditions and main macroeconomic parameters for the forecasting of socio-economic development in Russia in the near future implemented by the Ministry of Economic Development of the Russian Federation. The calculations reveal the existence of reserves for Russia’s “painless” participation in environment-preserving initiatives that call for not exceeding the 1990 emission level in 2020–2025. At the same time, increasing the environmental efficiency of Russia’s GDP is a relevant task that requires immediate attention. PubDate: 2017-10-01 DOI: 10.1007/s10598-017-9380-3 Issue No:Vol. 28, No. 4 (2017)

Authors:S. M. Orlov Pages: 561 - 571 Abstract: We consider the optimal control problem for a model of the spread of the influenza virus ignoring natural births and deaths. The problem is investigated by the Pontryagin maximum principle. A maximum principle boundary-value problem is constructed and it is analyzed numerically by the parameter continuation method. The best control is obtained in the class of piecewise-constant controls with one switching point, which is of definite interest in applications. The functional value under this control is worse by approximately 12.8% than the functional value under extremal control. PubDate: 2017-10-01 DOI: 10.1007/s10598-017-9381-2 Issue No:Vol. 28, No. 4 (2017)

Authors:E. N. Khailov; E. V. Grigorieva Pages: 572 - 605 Abstract: We consider a mathematical model describing a two-step process of wastewater biotreatment. This is a four-dimensional nonlinear system of differential equations with a scalar constraint on the control. The Pontryagin maximum principle is applied to investigate the boundary of the reachable set in this system. Among the possible parameter values and initial conditions of the model, we identify those for which piecewise-constant controls corresponding to boundary points of the reachable set have at most one, two, and three switching points. PubDate: 2017-10-01 DOI: 10.1007/s10598-017-9382-1 Issue No:Vol. 28, No. 4 (2017)

Authors:S. R. Tuikina; S. I. Solov’eva Pages: 301 - 309 Abstract: We consider the inverse problem for the two-dimensional modified FitzHugh–Nagumo model in the presence of an infarct. The inverse problem determines the myocardium excitation source function (a function of space variables and time) from a system of partial differential equations. Additional dynamic measurements of the potential are carried out on the entire inside boundary of the region representing a cross-section of the heart and its ventricles by a horizontal plane, which fits the real heart geometry. A numerical method is proposed for the solution of this inverse problem with the discrepancy functional; numerical results are reported. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9365-2 Issue No:Vol. 28, No. 3 (2017)

Authors:N. P. Savenkova; A. Yu. Mokin; V. P. Il’yutko Pages: 310 - 315 Abstract: We consider the dependence of the MHD stability of an electrolysis bath on the shape of the work space. As the optimal work-space shape we choose the one that achieves the best separation of the eigenvalues in the spectrum of the multidimensional problem posed for the kinematic equation for the electrolytealuminum interface in a particular electrolysis bath. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9366-1 Issue No:Vol. 28, No. 3 (2017)

Authors:Yu. N. Kiselev; S. N. Avvakumov; M. V. Orlov; S. M. Orlov Pages: 316 - 338 Abstract: We investigate the resource allocation problem in a two-sector economic model with a Cobb-Douglas production function with different depreciation rates. The problem is considered on a finite time horizon with an integral type functional. Optimality of the extremum solution constructed by the Pontryagin maximum principle is established. When the planning horizon is sufficiently long, the optimal control has two or three switching points, contains one singular section, and vanishes on the terminal section. A transitional “calibration” regime exists between the singular section, where the motion is along a singular ray, and the terminal section. The solution of the maximum-principle boundary-value problem is presented in explicit form, accompanied by graphs based on numerical results. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9367-0 Issue No:Vol. 28, No. 3 (2017)

Authors:A. M. Golovina; A. G. D’yakonov; O. A. Kharatsidi Pages: 339 - 349 Abstract: The article focuses on the analysis of photoplethysmograms. The quality of a photoplethysmogram is assessed by solving the classification problem, i.e., identifying the patient from the photoplethysmogram. Efficient patient identification methods are proposed, including methods based on DTW and TWED metrics. Identification accuracy reaches 70%. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9368-z Issue No:Vol. 28, No. 3 (2017)

Authors:Basant K. Jha; Babatunde Aina Pages: 350 - 367 Abstract: The present work consists of a numerical investigation of transient free convective flow in vertical channel formed by two infinite vertical parallel plates filled with porous material in the presence of thermal dispersion. The governing coupled-nonlinear equations of momentum and energy transport are solved numerically using the implicit finite difference method, while the approximate analytical solution is also presented to find the expression for velocity, temperature, skin friction, and rate of heat transfer for the steady fully developed flow using the perturbation technique. The main objective is to investigate the effects of the dimensionless time, Darcy number, thermal dispersion, and Prandtl number on the fluid flow and heat transfer characteristics. Solutions are presented in graphical form and given in terms of fluid velocity, fluid temperature, skin friction, and rate of heat transfer for various parametric values. The significant result from this study is that velocity and temperature is enhanced with increase in thermal dispersion parameter and time. Furthermore, excellent agreement is found between the steady-state solution and the transient solution at large values of time. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9369-y Issue No:Vol. 28, No. 3 (2017)

Authors:V. V. Morozov; V. A. Babin Pages: 368 - 376 Abstract: We consider a modified Merton’s model of optimal consumption that allows for the utility of continuous and terminal consumption. An explicit solution of the Hamilton-Jacoby-Bellman equation is found. An upper bound is constructed on the probability of an event involving either investor ruin or negative consumption. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9370-5 Issue No:Vol. 28, No. 3 (2017)

Authors:E. S. Kurkina Pages: 377 - 399 Abstract: We propose and investigate three mathematical models describing production cycles. They incorporate various mechanisms of endogenous fluctuations in economic systems. The models are based on ODE systems. The first model is a Keynesian IS-LM model of business cycles. The interest rate is determined by the money market and influences the relationship between savings and investments, allowing funds to flow from one to the other and vice versa. In the second case, the fluctuation mechanism is associated with time lags between investment growth, capital growth, and rate of return on capital. As a result, the economy periodically “overheats”, as rapid growth of capital suppresses the return rates, production becomes unprofitable, and investments sharply decline. Two models realizing this mechanism are proposed. One is a minimalist model based on a system of three ODEs. The other is an augmented model that sufficiently fully describes modern economic systems of developed countries and consists of nine ODEs and nine algebraic equations. It encompasses all the principal markets: labor market, capital market, financial market, and commodity market. Bifurcation analysis of the three models is carried out, oscillation regions are determined, and oscillation mechanisms are examined in detail. The model parameters are chosen so that the cycle periods are 12–17 years long. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9371-4 Issue No:Vol. 28, No. 3 (2017)

Authors:S. V. Gavrilov; S. I. Gurov; T. D. Zhukova; V. S. Rukhlov; D. I. Ryzhova; D. V. Tel’pukhov Pages: 400 - 406 Abstract: Increasing the operating reliability of integrated microcircuits (IMC) remains, on the whole, an unsolved design problem. An important aspect of this problem is the stability of the circuits under transient faults (malfunctions) in large integrated circuits. Faults appear due to various disturbances: radiation, supply voltage jumps, signal degradation over time, etc. Investigations show that the probability of an error due to these factors may vary between very wide limits: from less than 0.1% for large circuits and up to 30% for very small circuits. In this article, we consider various methods of enhancing the fault tolerance of combinational circuits and also assess the effect of a single fault and a stuck-at fault on circuit operation for the case of combinational circuits from the ISCAS’85 set. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9372-3 Issue No:Vol. 28, No. 3 (2017)

Authors:A. K. B. Chand; N. Vijender; M. A. Navascués Pages: 407 - 430 Abstract: Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C 1-smoothness of rational cubic FIFs render C 1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9373-2 Issue No:Vol. 28, No. 3 (2017)

Authors:Akanksha Srivastava Pages: 431 - 447 Abstract: This article deals with the study of sign-changing solutions of the nonlinear singularly perturbed reaction-diffusion equation. Sign changing solutions of the nonlinear problem do not appear to have been previously studied in detail computationally, and it is hoped that this paper will help to provide a new idea in this direction. A variant of Newton’s method having tenth order of convergence has been established to linearize the nonlinear system of equations. Examples of the nonlinear problem having nonlinearities in homogeneous/nonhomogeneous form are considered to show the existence of solutions. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9374-1 Issue No:Vol. 28, No. 3 (2017)

Authors:A. O. Novikova Abstract: A two-dimensional time-optimal problem with nonlinear gravity is investigated. The Pontryagin maximum principle is applied to solve the problem. The controllability set is investigated, the extremal control and the extremal time function are determined, optimality is proved by regular synthesis. PubDate: 2017-11-04 DOI: 10.1007/s10598-017-9376-z

Authors:Yu. N. Kiselev; S. N. Avvakumov; M. V. Orlov Abstract: We consider the resource allocation problem in a two-sector economy with a Constant Elasticity of Substitution (CES) production function on a given sufficiently long finite planning horizon. The performance criterion being optimized is one of the phase coordinates at the terminal time. The scalar control u satisfies the geometrical constraint u ∈ [0, 1]. The optimal control contains a singular section. Analyzing the Pontryagin maximum principle boundary-value problem we find the extremal triple and prove its optimality using a special representation of the functional increment (the theorem of sufficient conditions of optimality in terms of maximum-principle constructs). The solution is constructed with the aid of a Lambert special function y = W(x), that solves the equation ye y = x. The optimal control consists of three sections: the initial section that involves motion toward the singular ray L sng = {x 1 = x 2 > 0} , the singular section that involves motion along the singular ray, and terminal section that involves motion under zero control. When the initial state is on the singular ray, the optimal control consists of two sections — singular and terminal. The article is related to a number of the authors’ publications using other production function. PubDate: 2017-11-04 DOI: 10.1007/s10598-017-9375-0

Authors:Yu. A. Eremin Abstract: The optical theorem is generalized to the case of excitation of a local body by a multipole. To compute the extinction cross-section, it is sufficient to find the derivatives of the scattered field at the single point where the multipole is located. The relationship obtained in this article makes it possible to test software modules developed for studying wave diffraction on transparent bodies. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9354-5

Authors:Yang Jianxun Abstract: A new method for seismic data processing is considered. Surface traveling waves are recovered from these data and wave-dependent coefficients are determined. The results of the proposed method are consistent with the results reported by other Chinese researchers [4, 5]. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9361-6