LEADER 05123nam 22007335 450 001 9910163090003321 005 20220407215310.0 010 $a981-10-3180-0 024 7 $a10.1007/978-981-10-3180-9 035 $a(CKB)3710000001033356 035 $a(DE-He213)978-981-10-3180-9 035 $a(MiAaPQ)EBC4791116 035 $a(PPN)198338635 035 $a(EXLCZ)993710000001033356 100 $a20170124d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBifurcation in autonomous and nonautonomous differential equations with discontinuities /$fby Marat Akhmet, Ardak Kashkynbayev 205 $a1st ed. 2017. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2017. 215 $a1 online resource (XI, 166 p. 31 illus., 26 illus. in color.) 225 1 $aNonlinear Physical Science,$x1867-8440 311 $a981-10-3179-7 320 $aIncludes bibliographical references. 327 $aIntroduction -- Hopf Bifurcation in Impulsive Systems -- Hopf Bifurcation in Fillopov Systems -- Nonautonomous Transcritical and Pitchfork Bifurcations in an Impulsive Bernoulli Equations -- Nonautonomous Transcritical and Pitchfork Bifurcations in Scalar Non-solvable Impulsive Differential Equations -- Nonautonomous Transcritical and Pitchfork Bifurcations in Bernoulli Equations with Piecewise Constant Argument of Generalized Type. 330 $aThis book is devoted to bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types. That is, those with jumps present either in the right-hand-side or in trajectories or in the arguments of solutions of equations. The results obtained in this book can be applied to various fields such as neural networks, brain dynamics, mechanical systems, weather phenomena, population dynamics, etc. Without any doubt, bifurcation theory should be further developed to different types of differential equations. In this sense, the present book will be a leading one in this field. The reader will benefit from the recent results of the theory and will learn in the very concrete way how to apply this theory to differential equations with various types of discontinuity. Moreover, the reader will learn new ways to analyze nonautonomous bifurcation scenarios in these equations. The book will be of a big interest both for  beginners and experts in the field. For the former group of specialists, that is, undergraduate and graduate students, the book will be useful since it provides a strong impression that bifurcation theory can be developed not only for discrete and continuous systems, but those which combine these systems in very different ways. The latter group of specialists will find in this book several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impacts, differential equations with piecewise constant arguments of generalized type and Filippov systems. A significant benefit of the present book is expected to be for those who consider bifurcations in systems with impulses since they are presumably nonautonomous systems. 410 0$aNonlinear Physical Science,$x1867-8440 606 $aDynamics 606 $aErgodic theory 606 $aControl engineering 606 $aStatistical physics 606 $aDifference equations 606 $aFunctional equations 606 $aDifferential equations 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010 606 $aApplications of Nonlinear Dynamics and Chaos Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P33020 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aControl engineering. 615 0$aStatistical physics. 615 0$aDifference equations. 615 0$aFunctional equations. 615 0$aDifferential equations. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aControl and Systems Theory. 615 24$aApplications of Nonlinear Dynamics and Chaos Theory. 615 24$aDifference and Functional Equations. 615 24$aOrdinary Differential Equations. 676 $a510 700 $aAkhmet$b Marat$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478701 702 $aKashkynbayev$b Ardak$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910163090003321 996 $aBifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities$92000187 997 $aUNINA