. "Dynamics and Threshold Sets in Nonlinear Systems"@en . "Dynamika a prahov\u00E9 mno\u017Einy neline\u00E1rn\u00EDch syst\u00E9m\u016F"@cs . . . "We present a quantitative definition of a threshold that separates large-amplitude excitatory responses and small-amplitude nonexcitatory responses to a perturbation of an excitable system with a single globally attracting steady state. For systems with two variables, finding the threshold set is formulated as a boundary value problem supplemented by a condition of a maximum separation rate. For this highly nonlinear problem we formulate a numerical method based on the use of multiple shooting and continuation methods. The threshold phenomena are examined by using an example dynamical system with chemical reaction - the bromate-sulfite-ferrocyanide system. In a model of this reaction we find the threshold set, construct a bifurcation diagram and discuss how excitability can vanish. These results are compared with recent experiments."@en . . "Dynamics and Threshold Sets in Nonlinear Systems" . "excitable;perturbation;threshold;amplification"@en . . "7"^^ . . "561477" . "We present a quantitative definition of a threshold that separates large-amplitude excitatory responses and small-amplitude nonexcitatory responses to a perturbation of an excitable system with a single globally attracting steady state. For systems with two variables, finding the threshold set is formulated as a boundary value problem supplemented by a condition of a maximum separation rate. For this highly nonlinear problem we formulate a numerical method based on the use of multiple shooting and continuation methods. The threshold phenomena are examined by using an example dynamical system with chemical reaction - the bromate-sulfite-ferrocyanide system. In a model of this reaction we find the threshold set, construct a bifurcation diagram and discuss how excitability can vanish. These results are compared with recent experiments." . . "RIV/60461373:22340/04:00013206!RIV/2005/GA0/223405/N" . . . "22340" . "[F1366DA98B80]" . "Schreiber, Igor" . "RIV/60461373:22340/04:00013206" . "1" . . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "69" . "Vosla\u0159, Michal" . . . . "Navazuj\u00EDc na p\u0159edchoz\u00ED pr\u00E1ci [J. Zagora et al., Faraday Discuss. 120, 313 (2001)], navrhujeme kvantitativn\u00ED definici prahu odd\u011Bluj\u00EDc\u00EDho v excitabiln\u00EDch syst\u00E9mech s jedn\u00EDm stabiln\u00EDm stacion\u00E1rn\u00EDm stavem tlumen\u00E9 n\u00EDzkoamplitudov\u00E9 odezvy na perturbaci od excita\u010Dn\u00EDch odpov\u011Bd\u00ED s velkou amplitudou. Prahovou mno\u017Einu v syst\u00E9mech se dv\u011Bma prom\u011Bnn\u00FDmi hled\u00E1me jako \u0159e\u0161en\u00ED okrajov\u00E9 \u00FAlohy soustavy oby\u010Dejn\u00FDch diferenci\u00E1ln\u00EDch rovnic vyhovuj\u00EDc\u00ED podm\u00EDnce maxim\u00E1ln\u00ED separa\u010Dn\u00ED rychlosti. Obecn\u011B vysoce neline\u00E1rn\u00ED probl\u00E9m je \u0159e\u0161en numericky, spojen\u00EDm kontinua\u010Dn\u00EDho algoritmu s metodou v\u00EDcen\u00E1sobn\u00E9 st\u0159elby. Jako p\u0159\u00EDklad excitabiln\u00EDho syst\u00E9mu pou\u017E\u00EDv\u00E1me matematick\u00FD model chemick\u00E9ho oscil\u00E1toru bromi\u010Dnan-si\u0159i\u010Ditan-ferrokyanid, kde ukazujeme hled\u00E1n\u00ED prahov\u00E9 mno\u017Einy, sledujeme jej\u00ED v\u00FDvoj v z\u00E1vislosti na hodnot\u00E1ch opera\u010Dn\u00EDch parametr\u016F a zn\u00E1zor\u0148ujeme oblast existence excitability a jej\u00ED hranice v bifurka\u010Dn\u00EDm diagramu. V\u00FDsledky jsou porovn\u00E1ny s d\u0159\u00EDve publikovan\u00FDmi experimenty. S ohledem na pozorovan\u00E9 zp\u016Fsoby z\u00E1niku excitabiln\u00EDho chov\u00E1n\u00ED"@cs . "2"^^ . . "Physical Review E" . "Dynamics and Threshold Sets in Nonlinear Systems"@en . . . "Dynamika a prahov\u00E9 mno\u017Einy neline\u00E1rn\u00EDch syst\u00E9m\u016F"@cs . "026210-1 - 026210-7" . "P(GA203/03/0488), Z(MSM 223400007)" . "1063-651X" . "2"^^ . . "Dynamics and Threshold Sets in Nonlinear Systems" . .