The analytical properties of solutions of the generalized Rabinovich–Fabrikant system related to models of nonlinear physics and possessing certain qualitative properties at the values of its parameters are investigated.

1. Kuznetsov S. P., Turukina L. V. Generalized Rabinovich–Fabrikant system: equations and its dynamics. Izvestiya Vysshikh Uchebnykh Zavedeniy. Applied Nonlinear Dynamics, 2022, vol. 30, no. 1, pp. 7–29 (in Russian).

2. Rabinovich M. I., Fabrikant A. L. Stochastic self-samomudulation of waves in nonequilibrium media. Sov. Phys. JETP, 1979, vol. 77, no. 2, pp. 617–629 (in Russian).

3. Kuznetsov S. P. Dynamical Chaos. Moscow, Fizmatlit, 2006 (in Russian).

4. Danca M. F., Feskan M., Kuznetsov N., Chen G. Looking more closely to the Rabinovich– Fabrikant system. Int. J. Bifurc. Chaos, 2016, vol. 26, no. 2, art. 1650038.

5. Leonov G. A., Kuznetsov N. V. Hidden oscillations in dynamical systems. 16 Hilbert’s problem, Aizerman’s and Kalman’s conjectures, hidden attractors in Chua’s circuits. Modern Mathematics. Fundamental Direction, 2012, vol. 45, pp. 105–121 (in Russian).

6. Goriely A. Integrability and Singularity. Moscow, Izhevsk, Institute for Computer Research, 2006 (in Russian).

7. Ince E. L. Ordinary differential equations. Kharkov, GNTIU, 1939 (in Russian).

8. Gromak V. I., Lukashevich N. A. The Analytic Solutions of the Painleve´ Equations. Minsk, Universitetskoye, 1990 (in Russian).

9. Ablowitz M. J., Ramani A., Segur H. A connection between nonlinear evolution equations and ordinary differential equations of P-type. II. J. Math. Phys., 1980, vol. 21, pp. 715–721.

10. Ablowitz M. J., Segur H. Solitons and the Inverse Scattering Transform. Moscow, Mir, 1987 (in Russian).

11. Kowalevskaya S. V. Scientific Works. Moscow, Academiya nauk SSSR, 1948 (in Russian).

12. Gritsuk E. V., Gromak V. I. On the theory of nonlinear systems of differential equations with the Painleve´ property. Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series, 2010, no. 3, pp. 25–30 (in Russian).

13. Moon F. C. Chaotic Vibrations. Moscow, Mir, 1990 (in Russian).

14. Gromak V. I., Laine I., Shimomura S. Painleve´ Differential Equations in the Complex Plane. Berlin, de Gruyter, 2002.