Oscillations in Dynamic Systems with an Entropy Operator
Y. S. Popkov

Список литературы
1.	Popkov, Yu. S., “Theory of Dynamic Entropy-Operator Systems and Its Applications”, Autom. Remote Control, 67:6 (2006), 900–926
2.	Popkov, Yu. S., Mathematical Demoeconomy. Integrating Demographic and Economic Approaches, De Gruyter, Berlin, 2014, 500 pp.
3.	Shvetsov, V. I. and Helbing, D., “Macroscopic Dynamics of Multilane Traffic”, Phys. Rev. E, 59:6 (1999), 6328–6339
4.	Gasnikov, A. V., Dorn, Yu. V., Nesterov, Yu. E., and Shpirko, S. V., “On the Three-Stage Version of Stable Dynamic Model of Traffic Flows”, Matem. Model., 26:6 (2014), 34–70 (Russian)
5.	Popkov, A. Yu., Popkov, Yu. S., and van Wissen, L., “Positive Dynamic Systems with Entropy Operator: Application to Labour Market Modelling”, Eur. J. Oper. Res., 164:3 (2005), 811–828
6.	Popkov, Yu., Shvetsov, V., and Weidlich, W., “Settlement Formation Models with Entropy Operator”, Ann. Reg. Sci., 32:2 (1998), 267–294
7.	Leble, S. B., Vereshchagin, S. D., and Vereshchagina, I. S., “Algorithm for the Diagnostics of Waves and Entropy Mode in the Exponentially Stratified Atmosphere”, Russ. J. Phys. Chem. B, 14:2 (2020), 371–376
8.	Luckhaus, S. and Plotnikov, P. I., “Entropy Solutions to the Buckley – Leverett Equations”, Siberian Math. J., 41:2 (2000), 329–348        ; Sibirsk. Mat. Zh., 41:2 (2000), 400–420 (Russian)
9.	Popkov, Yu. S. and Rublev, M. V., “Dynamic Procedures of Image Reconstruction from Projections (Computer Tomography)”, Autom. Remote Control, 67:2 (2006), 233–241
10.	Daneev, A. V., Rusanov, V. A., and Sharpinskii, D. Yu., “The Entropy Maximum Principle in the Structural Identification of Dynamical Systems: An Analytic Approach”, Russian Math. (Iz. VUZ), 49:11 (2005), 14–22      ; Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 11, 16–24 (Russian)
11.	Tikhonov, A. N., Vasilieyva, A. B., and Volosov, V. M., “Differential Equations with Small Parameters”, Proc. of the Internat. Symp. on Nonlinear Oscillations (Kiev, Sep 1961), v. 1, 456–473 (Russian)
12.	Kurina, G. A., Dmitriev, M. G., and Naidu, D. S., “Discrete Singularly Pertubed Control Problems (A Survey)”, Discrete Continuous Dyn. Syst. Ser. B, 24 (2017), 335–370
13.	de Groot, S. E. and Masur, P., Non-Equilibrium Thermodynamics, North-Holland, Amsterdam, 1962, x, 510 pp.
14.	Popkov, Yu. S., “A New Class of Dynamic Macrosystem Models with Self-Reproduction”, Environ. Plan. A, 21:6 (1989), 739–751
15.	Wilson, A. G., Catastrophe Theory and Bifurcation: Applications to Urban and Regional Systems, Croom Helm, London, 1981, 354 pp.
16.	Bobylev, N. A. and Popkov, A. Yu., “Forced Oscillations in Systems with Argmin Type Operators”, Autom. Remote Control., 63:11 (2002), 1707–1716
17.	Antipin, A. S., “The Differential Controlled Gradient Method for Symmetric Extremal Mappings”, Differ. Equ., 34:8 (1998), 1020–1030      ; Differ. Uravn., 34:8 (1998), 1018–1028, 1148 (Russian)
18.	Popkov, A. Yu., Macrosystems Theory and Its Applications. Equilibrium Models, Lecture Notes Control Inform. Sci., 203, Springer, London, 1995, xiv+323 pp.
19.	Popkov, Yu. S., “Qualitative Analysis of Dynamic Systems with the $B_q^{}$ Entropy Operator”, Autom. Remote Control, 68:1 (2007), 38–53
20.	Popkov, Yu. S. and Rublev, M. V., “Estimation of a Local Lipschitz Constant of the $B_q^{}$-Entropy”, Autom. Remote Control, 66:7 (2005), 1069–1080
21.	Krasnosel'skii, M. A., Vainikko, G. M., Zabreiko, P. P., Rutitski, Ya. B., and Stecenko, V. Ya., Approximated Solutions of Operator Equations, Springer, Dordrecht, 1972, 496 pp.
22.	Krasnosel'skii, M. A., The Operator of Translation along the Trajectories of Differential Equations, Transl. Math. Monogr., 19, AMS, Providence, R.I., 1968, 294 pp.
23.	Bohr, H., “Zur Theorie der fastperiodischen Funktionen: 1. Eine Verallgemeinerung der Theorie der Fourierreihen”, Acta Math., 45 (1924), 29–127    ; Bohr, H., “Zur Theorie der fastperiodischen Funktionen: 2. Zusammenhang der fastperiodischen Funktionen mit Funktionen von unendlich vielen Variabeln; gleichmässige Approximation durch trigonometrische Summen”, Acta Math., 46 (1925), 102–214    ; Bohr, H., “Zur Theorie der fastperiodischen Funktionen: 3. Dirichletentwicklung analytischer Funktionen”, Acta Math., 47 (1926), 237–281
24.	Krasnosel'skii, M. A., Burd, V. S., and Kolesov, Yu. S., Nonlinear Almost Periodic Oscillations, Wiley, New York, 1973, 366 pp.
25.	Krasnosel'skii, M. A. and Zabreiko, P. P., Geometrical Methods of Nonlinear Analysis, Grundlehren Math. Wiss., 263, Springer, New York, 1984, XX, 412 pp.
26.	Popkov, Yu. S., “Upper Bound Design for the Lipschitz Constant of the $F_{G(\nu,\,q)}^{}$-Entropy Operator”, Mathematics, 6:5 (2018), 73, 9 pp.
27.	Davis, B., Integral Transforms and Their Applications, Springer, New York, 1978, xii, 411 pp.
28.	Tikhonov, A. N., Vasil'eva, A. B., and Sveshnikov, A. G., Differential Equations, Springer, Berlin, 1985, VIII, 240 pp.
29.	Beckenbach, E. F. and Bellman, R., Inequalities, Ergeb. Math. Grenzgeb. (N. F.), 30, Springer, Berlin, 1961, xii+198 pp.
30.	Malkin, I. G., Some Problems in the Theory of Nonlinear Oscillations: In 2 Vols., United States Atomic Energy Commission, Technical Information Service, Germantown, Md., 1959, 589 pp.
31.	Volterra, V., Theory of Functionals and Integro- and Integro-Differential Equations, Blackie & Son, London, 1930, iii, 226 pp.
32.	Popkov, Yu. S., Kiselev, O. N., Petrov, N. P., and Shmul'yan, B. L., Identification and Optimization of Nonlinear Stochastic Systems, Energiya, Moscow, 1976, 440 pp. (Russian)
33.	Ogunfunmi, T., Adaptive Nonlinear System Identification: The Volterra and Winer Approaches, Springer, New York, 2007, XVI, 232 pp.
34.	Van Trees, H. L., Synthesis of Optimal Nonlinear Control Systems, Cambridge, Mass., MIT, 102 pp.
35.	Debnath, L. and Bhatta, D., Integral Transforms and Their Applications, 3rd ed., CRC, Boca Raton, Fla., 2015, xxvi+792 pp.
36.	Polyak, B. T., Introduction to Optimization, Optimization Software, New York, 1987
37.	Magnus, J. R. and Neudecker, H., Matrix Differential Calculus with Applications in Statistics and Econometrics, 3rd ed., Wiley, New York, 2007