Tytuł pozycji:
Efficient choice of parameters on delta-reachability bounded hybrid systems
Hybrid systems (HS) are roughly described as a set of discrete state transitions and continuous dynamics modeled by differential equations. Parametric HS may be constructed by having parameters on the differential equations, initial conditions, jump conditions, or a combination of the previous ones. In real applications, the best solution is obtained by a set of metrics functional over the set of solutions generated from a finite set of parameters. This paper examines the choice of parameters on delta-reachability bounded hybrid systems. We present an efficient model based on the tool pHL-MT to benchmark the HS solutions (based on dReach), and a non-parametric frontier analysis approach, relying on multidirectional efficiency analysis (MEA). Three numerical examples of epidemic models with variable growth infectivity are presented, namely: when the variable of infected individuals oscillates around some endemic (non-autonomous) equilibrium; when there is an asymptotically stable non-trivial attractor; and in the presence of bump functions.
1. The authors were supported by the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020. Murillo was also supported by national funds (OE), through FCT, I.P., in the scope of the framework contract foreseen in the numbers 4, 5 and 6 of the article 23 of the Decree-Law 57/2016, of August 29, changed by Law 57/2017, of July 19.
2. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
