LEADER 05051nam 22006135 450 001 9910366620803321 005 20200703072600.0 010 $a3-030-20572-X 024 7 $a10.1007/978-3-030-20572-0 035 $a(CKB)4100000008493300 035 $a(DE-He213)978-3-030-20572-0 035 $a(MiAaPQ)EBC5796390 035 $a(PPN)242823467 035 $a(EXLCZ)994100000008493300 100 $a20190620d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlmost Periodicity, Chaos, and Asymptotic Equivalence /$fby Marat Akhmet 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XVII, 360 p. 26 illus., 25 illus. in color.) 225 1 $aNonlinear Systems and Complexity,$x2195-9994 ;$v27 311 $a3-030-19916-9 327 $aChapter 1. Introduction -- Chapter 2. Generalities for Impulsive systems -- Chapter 3. Discontinuous Almost Periodic Functions -- Chapter 4. Discontinuos Almost Periodic Solutions -- Chapter 5. Bohr and Bochner Discontinuities -- Chapter 6. Exponentially Dichotomous Linear EPCAG -- Chapter 7. Functional Response on Piecewise Constant Argument -- Chapter 8. SICNN with Functional REsponse on PCA -- Chapter 9. Differential Equations on Time SCales -- Chapter 10. Almost Periodicity in Chaos -- Chapter 11. Homoclinic Chaos and Almost Periodicity -- Chapter 12. SICNN with Chaotic/Almost Periodic Post Synaptic Currents -- Chapter 13. Asymptomatic Equivalence and Almost Periodic Soulutions -- Chapter 14. Asymptomatic Equivalence of Hybrid Systems. 330 $aThe central subject of this book is Almost Periodic Oscillations, the most common oscillations in applications and the most intricate for mathematical analysis. Prof. Akhmet's lucid and rigorous examination proves these oscillations are a "regular" component of chaotic attractors. The book focuses on almost periodic functions, first of all, as Stable (asymptotically) solutions of differential equations of different types, presumably discontinuous; and, secondly, as non-isolated oscillations in chaotic sets. Finally, the author proves the existence of Almost Periodic Oscillations (asymptotic and bi-asymptotic) by asymptotic equivalence between systems. The book brings readers' attention to contemporary methods for considering oscillations as well as to methods with strong potential for study of chaos in the future. Providing three powerful instruments for mathematical research of oscillations where dynamics are observable and applied, the book is ideal for engineers as well as specialists in electronics, computer sciences, robotics, neural networks, artificial networks, and biology. Distinctively combines results and methods of the theory of differential equations with thorough investigation of chaotic dynamics with almost periodic ingredients; Provides all necessary mathematical basics in their most developed form, negating the need for any additional sources for readers to start work in the area; Presents a unique method of investigation of discontinuous almost periodic solutions in its unified form, employed to differential equations with different types of discontinuity; Develops the equivalence method to its ultimate effective state such that most important theoretical problems and practical applications can be analyzed by the method. 410 0$aNonlinear Systems and Complexity,$x2195-9994 ;$v27 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aStatistical physics 606 $aDifferential equations 606 $aNeural networks (Computer science)  606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aApplications of Nonlinear Dynamics and Chaos Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P33020 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aMathematical Models of Cognitive Processes and Neural Networks$3https://scigraph.springernature.com/ontologies/product-market-codes/M13100 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aStatistical physics. 615 0$aDifferential equations. 615 0$aNeural networks (Computer science) . 615 14$aMathematical and Computational Engineering. 615 24$aApplications of Nonlinear Dynamics and Chaos Theory. 615 24$aOrdinary Differential Equations. 615 24$aMathematical Models of Cognitive Processes and Neural Networks. 676 $a519 676 $a515.5 700 $aAkhmet$b Marat$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478701 906 $aBOOK 912 $a9910366620803321 996 $aAlmost Periodicity, Chaos, and Asymptotic Equivalence$92539298 997 $aUNINA