PERIODIC SOLUTIONS OF IMPULSIVE SYSTEM OF DIFFERENTIAL EQUATIONS WITH MIXED MAXIMA

Benchohra M., Henderson J., Ntouyas S.K. Impulsive differential equations and inclusions. Contemporary mathematics and its application. Hindawi Publishing Corporation, New York, 2006.

Halanay A., Veksler D. Qualitative theory of impulsive systems. Mir, Moscow, 1971. 309 p. (in Russian).

Lakshmikantham V., Bainov D.D., Simeonov P.S. Theory of impulsive differential equations. World Scientific, Singapore, 1989. 434 p.

Perestyk N.A., Plotnikov V.A., Samoilenko A.M., Skripnik N.V. Differential equations with impulse effect: multivalued right-hand sides with discontinuities. DeGruyter Stud. 40, Math. Walter de Gruter Co., Berlin, 2011.

Samoilenko A.M., Perestyk N.A. Impulsive differential equations. World Sci., Singapore, 1995.

Stamova I., Stamov G. Impulsive biological models. In: Applied impulsive mathematical models. CMS Books in Mathematics. Springer, Cham. 2016.

Catlla J., Schaeffer D.G., Witelski Th.P., Monson E. E., Lin A.L. On spiking models for synaptic activity and impulsive differential equations. SIAM Review. 2008, 50 (3), P 553–569.

Fedorov E.G., Popov I.Yu. Analysis of the limiting behavior of a biological neurons system with delay. J. Phys.: Conf. Ser. 2021, 2086, 012109.

Fedorov E.G., Popov I.Yu. Hopf bifurcations in a network of Fitzhigh-Nagumo biological neurons. International Journal of Nonlinear Sciences and Numerical Simulation. 2021.

Fedorov E.G. Properties of an oriented ring of neurons with the FitzHugh-Nagumo model. Nanosystems: Phys. Chem. Math. 2021, 12 (5), P. 553– 562.

Anguraj A., Arjunan M.M. Existence and uniqueness of mild and classical solutions of impulsive evolution equations. Elect. J. of Differential Equations. 2005, 2005 (111), 1–8.

Ashyralyev A., Sharifov Y.A. Existence and uniqueness of solutions for nonlinear impulsive differential equations with two-point and integral boundary conditions. Advances in Difference Equations. 2013, 2013 (173).

Ashyralyev A., Sharifov Y.A. Optimal control problems for impulsive systems with integral boundary conditions. Elect. J. of Differential Equations. 2013, 2013 (80), 1–11.

Bin L., Xinzhi L., Xiaoxin L. Robust global exponential stability of uncertain impulsive systems. Acta Mathematika Scientia. 2005, 25 (1), P. 161– 169.

Mardanov M.J., Sharifov Ya.A., Habib M.H. Existence and uniqueness of solutions for first-order nonlinear differential equations with two-point and integral boundary conditions. Electr. J. of Differential Equations. 2014, 2014 (259), 1–8.

Sharifov Ya.A. Optimal control problem for systems with impulsive actions under nonlocal boundary conditions. Vestnik samarskogo gosudarstvennogo tekhnicheskogo universiteta. Seria: Fiziko-matematicheskie nauki. 2013, 33 (4), P. 34–45 (Russian).

Sharifov Ya.A. Optimal control for systems with impulsive actions under nonlocal boundary conditions. Russian Mathematics (Izv. VUZ). 2013, 57 (2), P. 65–72.

Sharifov Y.A., Mammadova N.B. Optimal control problem described by impulsive differential equations with nonlocal boundary conditions. Differential equations. 2014, 50 (3), P. 403–411.

Sharifov Y.A. Conditions optimality in problems control with systems impulsive differential equations with nonlocal boundary conditions. Ukrainain Math. Journ. 2012, 64 (6), P. 836–847.

Yuldashev T.K., Fayziev A.K. On a nonlinear impulsive differential equations with maxima. Bull. Inst. Math. 2021, 4 (6), P. 42–49.

Yuldashev T.K., Fayziev A.K. On a nonlinear impulsive system of integro-differential equations with degenerate kernel and maxima. Nanosystems: Phys. Chem. Math. 2022, 13 (1), P. 36–44.

Bai Ch., Yang D. Existence of solutions for second-order nonlinear impulsive differential equations with periodic boundary value conditions. Boundary Value Problems (Hindawi Publishing Corporation), 2007, 2007 (41589), 1–13.

Chen J., Tisdell Ch.C., Yuan R. On the solvability of periodic boundary value problems with impulse. J. of Math. Anal. and Appl. 2007, 331, P. 902–912.

Li X., Bohner M., Wang Ch.-K. Impulsive differential equations: Periodic solutions and applications. Automatica 2015, 52, P. 173–178.

Hu Z., Han M. Periodic solutions and bifurcations of first order periodic impulsive differential equations. International Journal of Bifurcation and Chaos. 2009, 19 (8), P. 2515–2530.

Samoilenko A.M., Perestyuk N.A. Periodic solutions of weakly nonlinear impulsive systems. Differentsial’nye uravneniya. 1978, 14 (6), P. 1034– 1045 (in Russian).

Yuldashev T. K. Periodic solutions for an impulsive system of nonlinear differential equations with maxima. Nonosystems: Physics, Chemistry, Mathematics. 2022, 13 (2), 135–141.

Yuldashev T.K. Periodic solutions for an impulsive system of integro-differential equations with maxima. Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки. 2022, 26 (2), 368–379.

Ma R., Yang B., Wang Z. Bifurcation of positive periodic solutions of first-order impulsive differential equations. Boundary Value Problems. 2012, 2012 (83), 1–16.

Gladilina R. I., Ignatyev A. O. On the stability of periodic impulsive systems. Math. Notes. 2004, 76 (1), P. 41–47.