## View abstract

### Session S25 - New Methods and Emerging Applications in Dynamics, Networks, and Control

Monday, July 12, 16:50 ~ 17:20 UTC-3

## Extension of the Solution Set of the Bounded Finite-Time Stabilization of the Prey-Predator Model via Controllability Function

### Abdon Choque-Rivero

#### Universidad Michoacana de San Nicolás de Hidalgo, México   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakafb843c95b1973dfed71356456d20f78').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyafb843c95b1973dfed71356456d20f78 = '&#97;bd&#111;n.ch&#111;q&#117;&#101;' + '&#64;'; addyafb843c95b1973dfed71356456d20f78 = addyafb843c95b1973dfed71356456d20f78 + '&#117;m&#105;ch' + '&#46;' + 'mx'; var addy_textafb843c95b1973dfed71356456d20f78 = '&#97;bd&#111;n.ch&#111;q&#117;&#101;' + '&#64;' + '&#117;m&#105;ch' + '&#46;' + 'mx';document.getElementById('cloakafb843c95b1973dfed71356456d20f78').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyafb843c95b1973dfed71356456d20f78 + '\'>'+addy_textafb843c95b1973dfed71356456d20f78+'<\/a>';

For the prey-predator model, an extended set of bounded finite-time stabilizing positional controls is given. We use Korobov’s controllability function $\Theta(x)$ which is a Lyapunov-type function. Previously, the controllability function was the unique solution of certain implicit equation on $\Theta$. In the present talk, we consider the case when there are between one and three solutions of the mentioned implicit equation. This occurs for initial positions belonging to certain domain of the phase space.