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010   $a3-030-22910-6
024 7 $a10.1007/978-3-030-22910-8
035   $a(CKB)4100000010122006
035   $a(DE-He213)978-3-030-22910-8
035   $a(MiAaPQ)EBC6033481
035   $a(PPN)242846742
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100   $a20200130d2019      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aBifurcation and Stability in Nonlinear Dynamical Systems /$fby Albert C. J. Luo
205   $a1st ed. 2019.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019.
215   $a1 online resource (IX, 395 p. 82 illus., 70 illus. in color.) 
225 1 $aNonlinear Systems and Complexity,$x2195-9994 ;$v28
311   $a3-030-22909-2 
327   $aStability of equilibriums -- Bifurcation of equilibriums -- Low-dimensional dynamical system -- Equilibrium and higher-singularity -- Low-degree polynomial systems -- (2m)th-degree polynomial systems -- (2m+1)th-degree polynomial systems -- Infinite-equilibrium systems.
330   $aThis book systematically presents a fundamental theory for the local analysis of bifurcation and stability of equilibriums in nonlinear dynamical systems. Until now, one does not have any efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums. For instance, infinite-equilibrium dynamical systems have higher-order singularity, which dramatically changes dynamical behaviors and possesses the similar characteristics of discontinuous dynamical systems. The stability and bifurcation of equilibriums on the specific eigenvector are presented, and the spiral stability and Hopf bifurcation of equilibriums in nonlinear systems are presented through the Fourier series transformation. The bifurcation and stability of higher-order singularity equilibriums are presented through the (2m)th and (2m+1)th -degree polynomial systems. From local analysis, dynamics of infinite-equilibrium systems is discussed. The research on infinite-equilibrium systems will bring us to the new era of dynamical systems and control. Presents an efficient way to investigate stability and bifurcation of dynamical systems with higher-order singularity equilibriums; Discusses dynamics of infinite-equilibrium systems; Demonstrates higher-order singularity.
410  0$aNonlinear Systems and Complexity,$x2195-9994 ;$v28
606   $aDifferential equations
606   $aVibration
606   $aDynamical systems
606   $aDynamics
606   $aComputational complexity
606   $aStatistical physics
606   $aPartial differential equations
606   $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147
606   $aVibration, Dynamical Systems, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/T15036
606   $aComplexity$3https://scigraph.springernature.com/ontologies/product-market-codes/T11022
606   $aApplications of Nonlinear Dynamics and Chaos Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P33020
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
615  0$aDifferential equations.
615  0$aVibration.
615  0$aDynamical systems.
615  0$aDynamics.
615  0$aComputational complexity.
615  0$aStatistical physics.
615  0$aPartial differential equations.
615 14$aOrdinary Differential Equations.
615 24$aVibration, Dynamical Systems, Control.
615 24$aComplexity.
615 24$aApplications of Nonlinear Dynamics and Chaos Theory.
615 24$aPartial Differential Equations.
676   $a515.355
676   $a515.352
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   $a9910370254003321
996   $aBifurcation and Stability in Nonlinear Dynamical Systems$91668175
997   $aUNINA