Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties
American Journal of Applied Mathematics
Volume 1, Issue 4, October 2013, Pages: 49-54
Received: Sep. 9, 2013;
Published: Oct. 30, 2013
Views 3117 Downloads 130
Sashka Petkova, University of Chemical Technology and Metallurgy, Sofia, Bulgaria
Andrey Antonov, University of Chemical Technology and Metallurgy, Sofia, Bulgaria
Rumyana Chukleva, Technical University of Sofia, Sofia, Bulgaria
The initial value problems for autonomous systems of differential equations are the main object of this paper. Different variants of the concept reachable sets for the solutions of such systems are introduced. Several conditions for their existence are found and some properties are studied.
Reachable Sets for Autonomous Systems of Differential Equations and their Topological Properties, American Journal of Applied Mathematics.
Vol. 1, No. 4,
2013, pp. 49-54.
D.Bainov, A.Dishliev,"Population dynamics control in regard to minimizing the time necessary for the regeneration of a biomass taken away from the population,"Applied Mathematics and Computation, Vol. 39, Issue 1, (1990), 37-48.
E.Coddington, N. Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, New York, Toronto, London, (1955).
A. Dishliev, K. Dishlieva, "Continuous dependence of the solutions of differential equations under "short" perturbations on the right–hand side," Communications in Applied Analysis, Vol. 10, Issue 2, (2006), 149-159.
A. Dishliev, K. Dishlieva, S. Nenov, Specific asymptotic properties of the solutions of impulsive differential equations. Methods and applications, Academic Publications, Ltd. (2012).
K. Dishlieva, "Impulsive differential equations and applications," J. Applied & Computational Mathematics, Vol. 1, Issue 6, (2012), 1-3.
K. Dishlieva, A. Dishliev, "Limitations of the solutions of differential equations with variable structure and impulses using sequences of Lyapunov functions," J. of Advanced Research in Applied Mathematics, Vol. 5, Issue 2, (2013), 39-52.
A. Dishliev, K. Dishlieva, "Orbital Hausdorff continuous dependence of the solutions of impulsive differential equations with respect to impulsive perturbations," International J. of Pure and Applied Mathematics, Vol. 70, Issue 2, (2011), 167-187.
S. Nenov, "Impulsive controllability and optimizations problems in population dynamics," Nonlinear Analysis, Vol. 36, Issue 7, (1999), 881-890.
L. Nie, Z. Teng, L. Hu, J. Peng, "The dynamics of a Lotka-Volterra predator-prey model with state dependent impulsive harvest for predator,"BioSystems, Vol. 98, Issue 2, (2009), 67-72.
Z. Shuai, L. Bai, K. Wang, "Optimization problems for general simple population with n-impulsive harvest," J. of Mathematical Analysis and Applications, Vol. 329, Issue 1, (2007), 634-646.
G. Stamov, Almost periodic solutions of impulsive differential equations, Springer, Heidelberg, New York, Dordrecht, London, (2012).
I. Stamova, G.-F.Emmenegger, "Stability of the solutions of impulsive functional differential equations modeling price fluctuations in single commodity markets," International J. of Applied Mathematics, Vol. 15, Issue 3,(2004), 271-290.
S. Tang, R. Cheke, Y. Xiao, "Optimal impulsive harvesting on non-autonomous Beverton-Holt difference equations," Nonlinear Analysis, Vol. 65, Issue 12, (2006), 2311-2341.
H. Wang, E. Feng, Z. Xiu, "Optimality control of the nonlinear impulsive system in fed-batch fermentation," Nonlinear Analysis: Theory, Methods & Applications, Vol. 68, Issue 1, (2008), 12-23.