Mathematical Modelling and Computing in Physics, Chemistry and Biology : Fundamentals and Applications / / Zdzislaw Trzaska

• Record Nr.: UNINA9910799228203321
• Autore: Trzaska Zdzisław
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, Springer Nature Switzerland AG, , [2023]; ©2023
• ISBN: 3-031-39985-4
• Edizione: [First edition.]
• Descrizione fisica: 1 online resource (320 pages)
• Collana: Studies in Systems, Decision and Control Series ; ; Volume 495
• Disciplina: 574.0113
• Soggetti: Biology - Computer simulation; Biology - Mathematical models; Chemistry - Computer simulation; Chemistry - Mathematical models
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Contents -- 1 Basic Characteristics of Dynamical Systems -- 1.1 Cornerstone -- 1.2 Concise Characterization of Complex Dynamical Systems -- 1.3 Relevance and Emergence of Natural Systems -- 1.4 Unusual Behavior of Complex Nonlinear Dynamical Systems -- 1.5 Entropy of Complex Processes in Dynamical Systems -- 1.6 Instantaneous States of Dynamical Systems -- References -- 2 Basic Ingredients of Nonlinear Systems Dynamics -- 2.1 Introduction -- 2.2 Nonlinear Phenomena and Nonlinear Equations -- 2.2.1 Preliminaries -- 2.2.2 Paradigmatic Nonlinear Models -- 2.2.3 Nonlinear Oscillators Solvable in Elementary Functions -- 2.3 Models of Complex Nonlinear Dynamic Systems -- 2.3.1 Basic Forms of Systems Oscillations -- 2.3.2 Systems Under Periodic Pulsed Excitation -- 2.3.3 Regular Periodic Pulses in Linear Systems -- 2.3.4 Oscillators Under the Periodic Impulsive Loading -- 2.3.5 Periodic Impulses with a Temporal 'Dipole' Shift -- 2.3.6 Fractional Order Differential Models -- 2.3.7 Artificial Intelligence Models -- 2.4 Mixed-Mode Oscillations -- 2.5 Stability and Bifurcation of Dynamic States -- 2.6 Chaotic Oscillations -- References -- 3 Oscillations in Physical Systems -- 3.1 Lorenz System and Its Properties -- 3.2 Logistic Equation and Its Applications -- 3.3 ; Predator-Prey Systems -- 3.4 Systems with the Double Scroll Attractors -- 3.5 Fractal Systems -- 3.6 Applications of Van der Pol Equation -- 3.7 The Rössler Attractor -- 3.8 Dynamic Analysis of the Nonlinear Energy Harvesting System -- 3.9 Duffing's Forced Oscillator -- References -- 4 Oscillatory Chemical Systems -- 4.1 Preliminary -- 4.2 Oscillations in Chemical Systems -- 4.3 Autocatalysis, Activation and Inhibition -- 4.4 Enzyme Kinetics -- 4.5 BZ Oscillating Reactions -- 4.6 Limit Cycle Oscillations in the BZ Reaction -- 4.7 Numerical Simulations of Kinetic Bistability of Reactions.; 4.8 Mathematical Modeling of Electrochemical Reactors -- 4.9 MMOs in Electrochemical Reactors -- References -- 5 Oscillations in Biological Processes -- 5.1 Motivation, Brief History and Background -- 5.2 Feedback Control Mechanisms -- 5.3 The Hodgkin-Huxley Neuron -- 5.3.1 Basic Mathematical Model -- 5.3.2 Periodic Neuron Firing -- 5.4 Reduced Model of a Single Neuron Activity -- 5.5 Nonlinear Human Cardiovascular System -- 5.5.1 Concise Characterization of a Cardiovascular System -- 5.5.2 Thermodynamic Model of the Cardiovascular System Dynamics -- 5.5.3 MMOs as an Indicator of Illness in the Cardiovascular System -- References -- 6 Energy Flow Analysis of Nonlinear Dynamical Systems -- 6.1 Introduction and Short Historical References -- 6.2 New Standards for the Energy Avenue in Non-sinusoidal States -- 6.2.1 Preliminary -- 6.2.2 Hysteresis Loops on Energy Phase Plane -- 6.2.3 Quantitative Measures of the Energy Hysteresis Loop -- 6.2.4 Estimates for One-Period Energy Loops -- 6.2.5 Analysis for Energy Aspects in Dynamical Systems with Switches -- 6.3 The Energy Approach to Electrochemical Corrosion Studies of Nano-copper Coatings -- 6.3.1 Introduction -- 6.3.2 The One-Period Energy Approach -- 6.3.3 Experiments -- 6.3.4 Results and Discussion -- 6.4 Effective Harvesting of Braking Energy in Electric Cars -- 6.4.1 Introduction -- 6.4.2 Energy Losses in Sub-systems of Electric Cars -- 6.4.3 Energy Regeneration in Sub-systems of Electric Cars -- 6.4.4 Modification of the Car Brake Sub-system -- 6.4.5 Regenerative Damping -- 6.4.6 Supercapacitor Characterization -- 6.4.7 Simulations -- 6.4.8 Summary and Conclusions -- 6.5 Electromechanical System for Charging Batteries of Electric Cars -- 6.5.1 Introduction -- 6.5.2 Principle of Batteries Charging with the Faraday Disk Generator -- 6.5.3 Battery Property and Modelling.; 6.5.4 Electro-magnetic-mechanical Model of Faraday Disk Generators -- 6.5.5 Structure of the Charging System -- 6.5.6 State-Space Equations -- 6.5.7 Computer Simulations -- 6.5.8 Discussion and Summary -- 6.6 Modeling of Energy Processes in Wheel-Rail Contacts Operating Under Influence of Periodic Discontinuous Forces -- 6.6.1 Introduction -- 6.6.2 The Problem Description -- 6.6.3 Dynamic Model of Wheel-Rail Contacts -- 6.6.4 Exact Periodic Solutions -- 6.6.5 Application of One-Period Energy Approach -- 6.6.6 Sleeper Nonlinear Characteristics -- 6.6.7 Discussion and Summary -- References -- 7 Artificial Intelligence in the Service of Dynamical Systems Studies -- 7.1 Background of AI Modeling -- 7.2 Common Types of AI Algorithms -- 7.3 Artificial Neural Network -- 7.3.1 Preliminary -- 7.3.2 Architectures of Artificial Neural Networks -- 7.3.3 Hopfield Artificial Neural Network -- 7.3.4 Equilibrium States in the Hopfield Network -- 7.4 Learning Neural Networks -- 7.5 Fuzzy Logic Models -- 7.5.1 Concise Overview -- 7.5.2 Fuzzy Systems -- 7.5.3 Building Fuzzy Models -- 7.5.4 Defuzzification -- 7.6 Real-Life Artificial Intelligence Applications -- References.