Contents 1. Introduction to dynamical systems .1 1.1. Cornerstone . 1 1.2. Concise Characterization of Natural Systems.
4 1.3. Relevance and Emergence of Natural Systems.7 1.4. Unusual Behavior of Complex Dynamical Systems . 9 1.5.
Entropy of Complex Processes in Dynamical Systems. 10 1.6. Instantaneous States of Dynamical Systems .13 References . 29 2. Basic ingredients of nonlinear systems dynamics 2.1.
Background.xx 2.2. Nonlinear Phenomena and Nonlinear Equations . xx 2.3. Mathematical Modeling of System Dynamics. xx 2.
3.1. Elementary Nonlinearities . xx 2.3.2. Nonlinear Oscillators Solvable in Elementary Functions . xx 2.
4. Models of Complex Nonlinear Dynamic Systems . xx 2.4.1. Basic forms of Systems Oscillations. xx 2.4.
2. Systems under Periodic Pulsed Excitation. xx 2.4.3. Regular Periodic Impulses . xx 2.4.
4. Harmonic Oscillator under the Periodic Impulsive Loading . xx 2.4.5. Periodic Impulses with a Temporal ''Dipole'' Shift . xx 2.4.
6. Fractional Order Differential Models .xx 2.4.7. Artificial intelligence models. xx 2.5.
Mixed-Mode Oscillations . xx 2.6. Stability and Bifurcation of Dynamic States . xx 2.7. Chaotic oscillations . xx References .
xx 3. Oscillations in physical systems . xx 3.1. Lorenz System and Its Properties . xx 3.2. Logistic Equation and Its Applications .
xx 3.3. Predator-Prey Systems . xx 3.4. The Two-Body Problem . xx 3.5.
Systems with the Double Scroll Attractors . xx 3.6. Applications of van der Pol Equation . xx 3.7. The Rössler Attractor . xx 3.
8. Furuta''s Pendulum Dynamics . xx 3.9. Dynamic Analysis of the Nonlinear Energy Harvesting System . xx 3.10. Duffing''s Forced oscillator .
xx 3.11. Chain of oscillators . xx 3.12. Oscillator with Weak or Strong Dissipation . xx 3.13.
VSI Fractional Dynamical System . xx 3.14. Characteristics of the Water Natural Hammer . xx 4. Oscillatory Chemical Systems .xx 4.1.
Preliminary . xx 4.2. Enzyme Kinetics . xx 4.3. Autocatalysis, Activation and Inhibition . xx 4.
4. Oscillations in Chemical Systems . xx 4.5. BZ Oscillating Reactions . xx 4.6. Limit Cycle Oscillations in the BZ Reaction .
xx 4.7. Numerical Simulations . xx 4.8. The Mathematical Model of Electrochemical Reactors . xx 4.9.
MMOs in Electrochemical Reactors . xx References . xx 5. Oscillations in Biological Processes . xx 5.1. Motivation, Brief History and Background . xx 5.
2. Feedback Control Mechanisms . xx 5.3. Parameter Space for Oscillations . xx 5.4. The Hodgkin-Huxley Neuron with MMOs .
xx 5.4.1. Basic Mathematical Model . xx 5.4.2. Periodic Neuron Firing .
xx 5.5. Reduced Model of a Single Neuron Activity . xx 5.6. Nonlinear Human Cardiovascular System . xx 5.6.
1. Concise Characterization of a Cardiovascular System . xx 5.6.2. Thermodynamic Model of the Cardiovascular System Dynamics . xx 5.6.
3. MMOs as an Indicator of Illness in the Cardiovascular System . xx 5.7. Models of Non-Linear DNA Dynamics . xx References . 6. Energy Flow Analysis of Nonlinear Dynamical Systems .
xx 6.1. Introduction and Short Historical References. xx 6.2. New Standards for the Energy Avenue in Non-Sinusoidal States . xx 6.2.
1. Preliminary. xx 6.2.2. Hysteresis Loops on Energy Phase Plane. xx 6.2.
3. Quantitative Measures of The Energy Hysteresis Loop. xx 6.2.4. Estimates for One-Period Energy Loops . xx 6.2.
5. Analysis for Energy Aspects in Dynamical Systems With Switches . xx 6.3. The Energy Approach to Electrochemical Corrosion Studies of Nano-Copper Coatings xx 6.3.1. Introduction .
xx 6.3.2. The One-Period Energy Approach . xx 6.3.3. Experiments .
xx 6.3.4. Results and Discussion . xx 6.4. Effective Harvesting of Braking Energy in Electric Cars . xx 6.
4.1. Introduction . xx 6.4.2. Energy Losses in Sub-Systems of Electric Cars . xx 6.
4.3. Energy Regeneration in Subsystems of Electric Cars . xx 6.4.4. Modification of the Car Brake Sub-System . xx 6.
4.7. Simulations . xx 6.4.8 Summary and Conclusions .