LEADER 03802nam 22007335 450 001 9910999784403321 005 20260204132909.0 010 $a9789819726172 010 $a9819726174 024 7 $a10.1007/978-981-97-2617-2 035 $a(CKB)38484928100041 035 $a(DE-He213)978-981-97-2617-2 035 $a(MiAaPQ)EBC32013224 035 $a(Au-PeEL)EBL32013224 035 $a(OCoLC)1515506296 035 $a(EXLCZ)9938484928100041 100 $a20250418d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLimit Cycles and Homoclinic Networks in Two-Dimensional Polynomial Systems /$fby Albert C. J. Luo 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (VIII, 316 p. 50 illus., 49 illus. in color.) 225 1 $aMathematics and Statistics Series 311 08$a9789819726165 311 08$a9819726166 327 $aIntroduction -- Homoclinic Networks without Centers -- Bifurcations for Homoclinic Networks without Centers -- Homoclinic Networks with Centers -- Bifurcations for Homoclinic Networks with Centers. 330 $aThis book is a monograph about limit cycles and homoclinic networks in polynomial systems. The study of dynamical behaviors of polynomial dynamical systems was stimulated by Hilbert?s sixteenth problem in 1900. Many scientists have tried to work on Hilbert's sixteenth problem, but no significant results have been achieved yet. In this book, the properties of equilibriums in planar polynomial dynamical systems are studied. The corresponding first integral manifolds are determined. The homoclinic networks of saddles and centers (or limit cycles) in crossing-univariate polynomial systems are discussed, and the corresponding bifurcation theory is developed. The corresponding first integral manifolds are polynomial functions. The maximum numbers of centers and saddles in homoclinic networks are obtained, and the maximum numbers of sinks, sources, and saddles in homoclinic networks without centers are obtained as well. Such studies are to achieve global dynamics of planar polynomial dynamical systems, which can help one study global behaviors in nonlinear dynamical systems in physics, chemical reaction dynamics, engineering dynamics, and so on. This book is a reference for graduate students and researchers in the field of dynamical systems and control in mathematics, mechanical, and electrical engineering. 410 0$aMathematics and Statistics Series 606 $aDynamics 606 $aSystem theory 606 $aControl theory 606 $aDifferential equations 606 $aDynamical Systems 606 $aSystems Theory, Control 606 $aComplex Systems 606 $aDifferential Equations 606 $aCicles límits$2thub 606 $aPolinomis$2thub 606 $aSistemes dinàmics diferenciables$2thub 608 $aLlibres electrònics$2thub 615 0$aDynamics. 615 0$aSystem theory. 615 0$aControl theory. 615 0$aDifferential equations. 615 14$aDynamical Systems. 615 24$aSystems Theory, Control. 615 24$aComplex Systems. 615 24$aDifferential Equations. 615 7$aCicles límits 615 7$aPolinomis 615 7$aSistemes dinàmics diferenciables. 676 $a515.39 700 $aLuo$b Albert C. J$4aut$4http://id.loc.gov/vocabulary/relators/aut$0720985 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910999784403321 996 $aLimit Cycles and Homoclinic Networks in Two-Dimensional Polynomial Systems$94375009 997 $aUNINA