LEADER 04063nam 22006375 450 001 9910983084603321 005 20250227005429.0 010 $a9783031689666 010 $a3031689666 024 7 $a10.1007/978-3-031-68966-6 035 $a(MiAaPQ)EBC31738058 035 $a(Au-PeEL)EBL31738058 035 $a(CKB)36389222800041 035 $a(DE-He213)978-3-031-68966-6 035 $a(OCoLC)1463766865 035 $a(EXLCZ)9936389222800041 100 $a20241023d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aArtificial Neural Networks $eAlpha Unpredictability and Chaotic Dynamics /$fby Marat Akhmet, Madina Tleubergenova, Akylbek Zhamanshin, Zakhira Nugayeva 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (256 pages) 311 08$a9783031689659 311 08$a3031689658 327 $aPreface -- 1. Introduction -- 2. Preliminaries -- 3. Hopfield-type neural networks -- 4. Shunting inhibitory cellular neural networks -- 5. Inertial neural networks with discontinuities -- 6. Cohen-Grossberg neural networks. 330 $aMathematical chaos in neural networks is a powerful tool that reflects the world?s complexity and has the potential to uncover the mysteries of the brain?s intellectual activity. Through this monograph, the authors aim to contribute to modern chaos research, combining it with the fundamentals of classical dynamical systems and differential equations. The readers should be reassured that an in-depth understanding of chaos theory is not a prerequisite for working in the area designed by the authors. Those interested in the discussion can have a basic understanding of ordinary differential equations and the existence of bounded solutions of quasi-linear systems on the real axis. Based on the novelties, this monograph aims to provide one of the most powerful approaches to studying complexities in neural networks through mathematical methods in differential equations and, consequently, to create circumstances for a deep comprehension of brain activity and artificial intelligence. A large part of the book consists of newly obtained contributions to the theory of recurrent functions, Poisson stable, and alpha unpredictable solutions and ultra Poincaré chaos of quasi-linear and strongly nonlinear neural networks such as Hopfield neural networks, shunting inhibitory cellular neural networks, inertial neural networks, and Cohen-Grossberg neural networks. The methods and results presented in this book are meant to benefit senior researchers, engineers, and specialists working in artificial neural networks, machine and deep learning, computer science, quantum computers, and applied and pure mathematics. This broad applicability underscores the value and relevance of this research area to a large academic community and the potential impact it can have on various fields. . 606 $aArtificial intelligence 606 $aMachine learning 606 $aNeural networks (Computer science) 606 $aArtificial Intelligence 606 $aMachine Learning 606 $aMathematical Models of Cognitive Processes and Neural Networks 606 $aStatistical Learning 615 0$aArtificial intelligence. 615 0$aMachine learning. 615 0$aNeural networks (Computer science) 615 14$aArtificial Intelligence. 615 24$aMachine Learning. 615 24$aMathematical Models of Cognitive Processes and Neural Networks. 615 24$aStatistical Learning. 676 $a006.3 700 $aAkhmet$b Marat$0478701 701 $aTleubergenova$b Madina$01785854 701 $aZhamanshin$b Akylbek$01785855 701 $aNugayeva$b Zakhira$01785856 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910983084603321 996 $aArtificial Neural Networks$94317306 997 $aUNINA