Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
Advances in analysis and control of time-delayed dynamical systems / / edited by Jian-Qiao Sun, Qiang Ding
| Advances in analysis and control of time-delayed dynamical systems / / edited by Jian-Qiao Sun, Qiang Ding |
| Pubbl/distr/stampa | Singapore : , : World Scientific Publishing Company, , [2013] |
| Descrizione fisica | 1 online resource (355 p.) |
| Disciplina | 629.83 |
| Altri autori (Persone) |
DingQiang
SunJian-Qiao |
| Soggetto topico |
Feedback control systems
Time delay systems |
| Soggetto genere / forma | Electronic books. |
| ISBN | 981-4525-50-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Chapter 1 Complete Quadratic Lyapunov-Krasovskii Functional: Limitations, Computational Efficiency, and Convergence Keqin Gu; 1. Introduction; 2. Complete Quadratic Lyapunov-Krasovskii Functional; 3. Discretized Lyapunov Functional Method; 4. Coupled Differential-difference Equations; 5. Miscellaneous Issues; 5.1. Computational Efficiency; 5.2. Convergence Issue for Multiple Neutral Delays; 5.3. Lyapunov-Krasovskii Functionals Containing State Derivatives; 6. SOS Method; 7. Conclusions and Perspectives; References
Chapter 2 Recent Approaches for the Numerical Solution of State-dependent Delay Differential Equations with Discontinuities Alfredo Bellen1. Introduction; 2. Weak Solutions; 3. Regularization Techniques; 4. Comparing Regularizations; References; Chapter 3 Engineering Applications of Time-periodic Time-delayed Systems Gabor Stepan; 1. Introduction; 2. Delayed Mathieu Equation; 3. Semi-discretization Method for Periodic DDEs; 4. Engineering Applications; 4.1. Modeling and Stability of Milling Operations; 4.2. Cutting with Varying Spindle Speed 4.3. Act-and-wait Control of Force Controlled Robots5. Conclusions; References; Chapter 4 Synchronization in Delay-coupled Complex Networks Eckehard Scholl; 1. Introduction; 2. Stability of Synchronization for Large Delay; 3. Cluster Synchronization; 4. Adaptive Synchronization; 4.1. Speed-gradient Method; 4.2. Zero-lag Synchronization; 4.3. Splay State and Cluster Synchronization; 4.4. Controlling Several Parameters Simultaneously; 5. Transitions between Synchronization and Desychronization; 5.1. Excitability of Type II; 5.2. Excitability of Type I; 6. Conclusion and Outlook; References Chapter 5 Stochastic Dynamics and Optimal Control of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control Weiqiu Zhu, Zhonghua Liu1. Introduction; 2. Stochastic Averaging Method for Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control; 2.1. Gaussian White Noise Excitations; 2.1.1. Non-resonant Case; 2.1.2. Resonant Case; 2.2. Wide-band Random Excitations; 2.2.1. Non-resonant Case; 2.2.2. Resonant Case; 2.3. Narrow-band Bounded Noise Excitation; 2.3.1. External Resonance Only; 2.3.2. Both Internal and External Resonances 2.4. Combined Excitations of Harmonic Function and One Kind of above Random Processes2.4.1. Internal Resonance Only; 2.4.2. External Resonance Only; 2.4.3. Both Internal and External Resonances; 3. Stochastic Dynamics of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control; 3.1. Response; 3.2. Stochastic Stability; 3.3. Stochastic Bifurcation; 3.4. First Passage Failure; 3.4.1. Gaussian White Noise Excitation; 4. Stochastic Optimal Control of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control; 4.1. Response Minimization Control; 4.2. Stabilization 4.3. Minimax Optimal Bounded Control |
| Record Nr. | UNINA-9910453633703321 |
| Singapore : , : World Scientific Publishing Company, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Advances in analysis and control of time-delayed dynamical systems / / edited by Jian-Qiao Sun, Univeristy of California-Merced, USA, Qian Ding, Tianjin University, China
| Advances in analysis and control of time-delayed dynamical systems / / edited by Jian-Qiao Sun, Univeristy of California-Merced, USA, Qian Ding, Tianjin University, China |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2013] |
| Descrizione fisica | 1 online resource (x, 342 pages) : illustrations (some color) |
| Disciplina | 629.83 |
| Collana | Gale eBooks |
| Soggetto topico |
Dynamics
Time delay systems |
| ISBN | 981-4525-50-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Chapter 1 Complete Quadratic Lyapunov-Krasovskii Functional: Limitations, Computational Efficiency, and Convergence Keqin Gu; 1. Introduction; 2. Complete Quadratic Lyapunov-Krasovskii Functional; 3. Discretized Lyapunov Functional Method; 4. Coupled Differential-difference Equations; 5. Miscellaneous Issues; 5.1. Computational Efficiency; 5.2. Convergence Issue for Multiple Neutral Delays; 5.3. Lyapunov-Krasovskii Functionals Containing State Derivatives; 6. SOS Method; 7. Conclusions and Perspectives; References
Chapter 2 Recent Approaches for the Numerical Solution of State-dependent Delay Differential Equations with Discontinuities Alfredo Bellen1. Introduction; 2. Weak Solutions; 3. Regularization Techniques; 4. Comparing Regularizations; References; Chapter 3 Engineering Applications of Time-periodic Time-delayed Systems Gabor Stepan; 1. Introduction; 2. Delayed Mathieu Equation; 3. Semi-discretization Method for Periodic DDEs; 4. Engineering Applications; 4.1. Modeling and Stability of Milling Operations; 4.2. Cutting with Varying Spindle Speed 4.3. Act-and-wait Control of Force Controlled Robots5. Conclusions; References; Chapter 4 Synchronization in Delay-coupled Complex Networks Eckehard Scholl; 1. Introduction; 2. Stability of Synchronization for Large Delay; 3. Cluster Synchronization; 4. Adaptive Synchronization; 4.1. Speed-gradient Method; 4.2. Zero-lag Synchronization; 4.3. Splay State and Cluster Synchronization; 4.4. Controlling Several Parameters Simultaneously; 5. Transitions between Synchronization and Desychronization; 5.1. Excitability of Type II; 5.2. Excitability of Type I; 6. Conclusion and Outlook; References Chapter 5 Stochastic Dynamics and Optimal Control of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control Weiqiu Zhu, Zhonghua Liu1. Introduction; 2. Stochastic Averaging Method for Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control; 2.1. Gaussian White Noise Excitations; 2.1.1. Non-resonant Case; 2.1.2. Resonant Case; 2.2. Wide-band Random Excitations; 2.2.1. Non-resonant Case; 2.2.2. Resonant Case; 2.3. Narrow-band Bounded Noise Excitation; 2.3.1. External Resonance Only; 2.3.2. Both Internal and External Resonances 2.4. Combined Excitations of Harmonic Function and One Kind of above Random Processes2.4.1. Internal Resonance Only; 2.4.2. External Resonance Only; 2.4.3. Both Internal and External Resonances; 3. Stochastic Dynamics of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control; 3.1. Response; 3.2. Stochastic Stability; 3.3. Stochastic Bifurcation; 3.4. First Passage Failure; 3.4.1. Gaussian White Noise Excitation; 4. Stochastic Optimal Control of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control; 4.1. Response Minimization Control; 4.2. Stabilization 4.3. Minimax Optimal Bounded Control |
| Record Nr. | UNINA-9910790837003321 |
| New Jersey : , : World Scientific, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Advances in analysis and control of time-delayed dynamical systems / / edited by Jian-Qiao Sun, Univeristy of California-Merced, USA, Qian Ding, Tianjin University, China
| Advances in analysis and control of time-delayed dynamical systems / / edited by Jian-Qiao Sun, Univeristy of California-Merced, USA, Qian Ding, Tianjin University, China |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2013] |
| Descrizione fisica | 1 online resource (x, 342 pages) : illustrations (some color) |
| Disciplina | 629.83 |
| Collana | Gale eBooks |
| Soggetto topico |
Dynamics
Time delay systems |
| ISBN | 981-4525-50-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Chapter 1 Complete Quadratic Lyapunov-Krasovskii Functional: Limitations, Computational Efficiency, and Convergence Keqin Gu; 1. Introduction; 2. Complete Quadratic Lyapunov-Krasovskii Functional; 3. Discretized Lyapunov Functional Method; 4. Coupled Differential-difference Equations; 5. Miscellaneous Issues; 5.1. Computational Efficiency; 5.2. Convergence Issue for Multiple Neutral Delays; 5.3. Lyapunov-Krasovskii Functionals Containing State Derivatives; 6. SOS Method; 7. Conclusions and Perspectives; References
Chapter 2 Recent Approaches for the Numerical Solution of State-dependent Delay Differential Equations with Discontinuities Alfredo Bellen1. Introduction; 2. Weak Solutions; 3. Regularization Techniques; 4. Comparing Regularizations; References; Chapter 3 Engineering Applications of Time-periodic Time-delayed Systems Gabor Stepan; 1. Introduction; 2. Delayed Mathieu Equation; 3. Semi-discretization Method for Periodic DDEs; 4. Engineering Applications; 4.1. Modeling and Stability of Milling Operations; 4.2. Cutting with Varying Spindle Speed 4.3. Act-and-wait Control of Force Controlled Robots5. Conclusions; References; Chapter 4 Synchronization in Delay-coupled Complex Networks Eckehard Scholl; 1. Introduction; 2. Stability of Synchronization for Large Delay; 3. Cluster Synchronization; 4. Adaptive Synchronization; 4.1. Speed-gradient Method; 4.2. Zero-lag Synchronization; 4.3. Splay State and Cluster Synchronization; 4.4. Controlling Several Parameters Simultaneously; 5. Transitions between Synchronization and Desychronization; 5.1. Excitability of Type II; 5.2. Excitability of Type I; 6. Conclusion and Outlook; References Chapter 5 Stochastic Dynamics and Optimal Control of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control Weiqiu Zhu, Zhonghua Liu1. Introduction; 2. Stochastic Averaging Method for Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control; 2.1. Gaussian White Noise Excitations; 2.1.1. Non-resonant Case; 2.1.2. Resonant Case; 2.2. Wide-band Random Excitations; 2.2.1. Non-resonant Case; 2.2.2. Resonant Case; 2.3. Narrow-band Bounded Noise Excitation; 2.3.1. External Resonance Only; 2.3.2. Both Internal and External Resonances 2.4. Combined Excitations of Harmonic Function and One Kind of above Random Processes2.4.1. Internal Resonance Only; 2.4.2. External Resonance Only; 2.4.3. Both Internal and External Resonances; 3. Stochastic Dynamics of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control; 3.1. Response; 3.2. Stochastic Stability; 3.3. Stochastic Bifurcation; 3.4. First Passage Failure; 3.4.1. Gaussian White Noise Excitation; 4. Stochastic Optimal Control of Quasi Integrable Hamiltonian Systems with Time-delayed Feedback Control; 4.1. Response Minimization Control; 4.2. Stabilization 4.3. Minimax Optimal Bounded Control |
| Record Nr. | UNINA-9910815733903321 |
| New Jersey : , : World Scientific, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Complex-valued neural networks systems with time delay : stability analysis and (anti-)synchronization control / / Ziye Zhang [and three others]
| Complex-valued neural networks systems with time delay : stability analysis and (anti-)synchronization control / / Ziye Zhang [and three others] |
| Autore | Zhang Ziye |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (236 pages) |
| Disciplina | 006.32 |
| Collana | Intelligent Control and Learning Systems |
| Soggetto topico |
Neural networks (Computer science)
Time delay systems |
| ISBN | 981-19-5450-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Symbols -- 1 Introduction -- 1.1 History of Neural Networks -- 1.2 History of Complex-Valued Neural Networks -- 1.3 Recent Progress of Complex-Valued Neural Networks -- 1.3.1 Survey of Dynamics of CVNNs -- 1.3.2 Survey of Dynamics of CVBAMNNs -- 1.3.3 Survey of Dynamics of CVINNs -- 1.4 This Book -- References -- 2 Stability Criterion for CVNNs with Constant Delay -- 2.1 Introduction -- 2.2 Problem Formulation -- 2.3 Main Result -- 2.4 Illustrative Examples -- 2.5 Conclusion -- References -- 3 Further Stability Analysis for CVNNs with Constant Delay -- 3.1 Introduction -- 3.2 Preliminaries -- 3.3 Further Stability Analysis Based on Separable Method -- 3.4 Stability Analysis Based on Nonseparable Method -- 3.5 Illustrative Examples -- 3.6 Conclusion and Notes -- References -- 4 Hopf Bifurcation Analysis for CVNNs with Discrete and Distributed Delays -- 4.1 Introduction -- 4.2 Problem Formulation -- 4.3 Hopf Bifurcation Result -- 4.4 Direction of the Hopf Bifurcation -- 4.5 Illustrative Example -- 4.6 Conclusion -- References -- 5 Finite-Time Stability Analysis for CVBAMNNs with Constant Delay -- 5.1 Introduction -- 5.2 Problem Formulation and Preliminaries -- 5.3 Sufficient Criterion for the Existence and Uniqueness -- 5.4 Finite-Time Stability Criterion -- 5.5 Illustrative Examples -- 5.6 Conclusion -- References -- 6 Lagrange Exponential Stability for CVBAMNNs with Time-Varying Delays -- 6.1 Introduction -- 6.2 Problem Formulation and Preliminaries -- 6.3 Stability Criteria Based on Algebraic Structure -- 6.3.1 Stability Criterion Dependent on Separable Method -- 6.3.2 Stability Criterion Dependent on Nonseparable Method -- 6.4 Stability Criterion in Terms of LMI -- 6.5 Illustrative Examples -- 6.6 Conclusion -- References -- 7 Anti-synchronization Control for CVBAMNNs with Time-Varying Delays -- 7.1 Introduction.
7.2 Problem Formulation and Preliminaries -- 7.3 Anti-Synchronization Control Criterion -- 7.4 Illustrative Example -- 7.5 Conclusion -- References -- 8 Anti-synchronization Control for CVNNs with Mixed Delays -- 8.1 Introduction -- 8.2 Problem Formulation and Preliminaries -- 8.3 Anti-synchronization Criterion Based on Separable Method -- 8.4 Anti-synchronization Criterion Based on Nonseparable Method -- 8.5 Illustrative Examples -- 8.6 Conclusion -- References -- 9 (Anti)-Synchronization for CVINNs with Time-Varying Delays -- 9.1 Introduction -- 9.2 Problem Formulation and Preliminaries -- 9.3 Synchronization Control Criterion -- 9.4 Anti-Synchronization Control Criterion -- 9.5 Illustrative Examples -- 9.6 Conclusion -- References -- 10 Fixed-Time Synchronization for CVBAMNNs with Time Delays -- 10.1 Introduction -- 10.2 Problem Formulation and Preliminaries -- 10.3 Fixed-Time Synchronization Criterion -- 10.4 Illustrative Examples -- 10.5 Conclusion -- References -- 11 Fixed-Time Pinning Synchronization for CVINNs with Time-Varying Delays -- 11.1 Introduction -- 11.2 Problem Formulation and Preliminaries -- 11.3 Main Results -- 11.3.1 Fixed-Time Synchronization Criterion -- 11.3.2 Fixed-Time Adaptive Synchronization Criterion -- 11.4 Illustrative Example -- 11.5 Conclusion -- References -- Index. |
| Record Nr. | UNISA-996499864203316 |
Zhang Ziye
|
||
| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Delay systems : from theory to numerics and applications / / Tomas Vyhlidal, Jean-Francois Lafay, Rifat Sipahi, editors
| Delay systems : from theory to numerics and applications / / Tomas Vyhlidal, Jean-Francois Lafay, Rifat Sipahi, editors |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , 2014 |
| Descrizione fisica | 1 online resource (xxiv, 404 pages) : illustrations (some color) |
| Disciplina | 620 |
| Collana | Advances in Delays and Dynamics |
| Soggetto topico | Time delay systems |
| ISBN | 3-319-01695-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I Stability Analysis and Control Design -- Part II Networks and Graphs -- Part III Time-Delay and Sampled-Data Systems -- Part IV Computational and software tools -- Part V Applications. |
| Record Nr. | UNINA-9910299479403321 |
| Cham, Switzerland : , : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Model predictive control for nonlinear continuous-time systems with and without time-delays / / vorgelegt von Marcus Reble
| Model predictive control for nonlinear continuous-time systems with and without time-delays / / vorgelegt von Marcus Reble |
| Autore | Reble Marcus |
| Pubbl/distr/stampa | Berlin : , : Logos, , [2013] |
| Descrizione fisica | 1 online resource (162 pages) |
| Disciplina | 629.8 |
| Soggetto topico |
Predictive control
Time delay systems |
| Soggetto genere / forma | Electronic books. |
| ISBN | 3-8325-9362-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910467771703321 |
|
Reble Marcus
|
||
| Berlin : , : Logos, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Model predictive control for nonlinear continuous-time systems with and without time-delays / / vorgelegt von Marcus Reble
| Model predictive control for nonlinear continuous-time systems with and without time-delays / / vorgelegt von Marcus Reble |
| Autore | Reble Marcus |
| Pubbl/distr/stampa | Berlin : , : Logos, , [2013] |
| Descrizione fisica | 1 online resource (162 pages) |
| Disciplina | 629.8 |
| Soggetto topico |
Predictive control
Time delay systems |
| ISBN | 3-8325-9362-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910795453803321 |
|
Reble Marcus
|
||
| Berlin : , : Logos, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Model predictive control for nonlinear continuous-time systems with and without time-delays / / vorgelegt von Marcus Reble
| Model predictive control for nonlinear continuous-time systems with and without time-delays / / vorgelegt von Marcus Reble |
| Autore | Reble Marcus |
| Pubbl/distr/stampa | Berlin : , : Logos, , [2013] |
| Descrizione fisica | 1 online resource (162 pages) |
| Disciplina | 629.8 |
| Soggetto topico |
Predictive control
Time delay systems |
| ISBN | 3-8325-9362-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910823657203321 |
|
Reble Marcus
|
||
| Berlin : , : Logos, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
PID controllers for time-delay systems / Guillermo J. Silva, Aniruddha Datta, S.P. Bhattacharyya
| PID controllers for time-delay systems / Guillermo J. Silva, Aniruddha Datta, S.P. Bhattacharyya |
| Autore | Silva, G. J., 1973- |
| Pubbl/distr/stampa | Boston ; Basel ; Berlin : Birkhèauser, c2005 |
| Descrizione fisica | xii, 330 p. : ill. ; 25 cm |
| Disciplina | 629.83 |
| Altri autori (Persone) |
Datta, Aniruddha, 1963-author
Bhattacharyya, Shankar P., 1946- |
| Collana | Control engineering [Birkhauser] |
| Soggetto topico |
PID controllers - Design and construction
Time delay systems |
| ISBN | 0817642668 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001379769707536 |
|
Silva, G. J., 1973-
|
||
| Boston ; Basel ; Berlin : Birkhèauser, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Stochastic systems with time delay : probabilistic and thermodynamic descriptions of non-Markovian processes far from equilibrium / / Sarah A.M. Loos
| Stochastic systems with time delay : probabilistic and thermodynamic descriptions of non-Markovian processes far from equilibrium / / Sarah A.M. Loos |
| Autore | Loos Sarah A. M. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (296 pages) |
| Disciplina | 003.76 |
| Collana | Springer Theses |
| Soggetto topico |
Stochastic systems
Time delay systems Thermodynamics - Mathematics Sistemes estocàstics Termodinàmica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-80771-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Supervisor's Foreword -- Abstract -- Acknowledgements -- Publications by Sarah A. M. Loos -- Contents -- Abbreviations and Symbols -- Abbreviations -- Symbols -- 1 Introduction -- 1.1 Outline of the Thesis -- References -- Part I Theoretical Background and State of the Art -- 2 The Langevin Equation -- 2.1 The Stochastic Way of Describing Things -- 2.1.1 Brownian Motion -- 2.1.2 Colloidal Suspensions -- 2.1.3 Side Note: A More General View -- 2.2 The Markovian Langevin Equation -- 2.2.1 Gaussian White Noise -- 2.2.2 Ensemble Averages and Probability Density -- 2.2.3 Solutions of the Langevin Equation and the Overdamped Limit -- 2.2.4 Ornstein-Uhlenbeck Process -- 2.2.5 White Noise-Wiener Process-Stochastic Calculus -- 2.2.6 Path Integral Representation -- 2.3 Generalised Langevin Equations-How Stochastic Motion … -- 2.3.1 Infinite Harmonic Oscillators Bath-An Example of a Mori-Zwanzig Projection -- 2.3.2 Coarse-Graining-Forgetting Some Details -- 2.3.3 Side Node: Taking this Simplified Model Serious -- 2.3.4 The Markov Assumption -- 2.3.5 Real-World Complications -- 2.3.6 Time-Reversal Symmetry and Causality -- 2.4 Introduction to the Langevin Equation with Time Delay -- 2.4.1 Optical Traps-An Experimental Tool to Control -- 2.4.2 Time-Delayed Feedback -- 2.4.3 The Langevin Equation with Time Delay -- 2.4.4 Side Note: Delay Differential Equations -- 2.4.5 Linear Systems with Time Delay -- 2.5 Nonlinear Example Systems with Time Delay -- 2.5.1 Bistable System: The Doublewell Potential -- 2.5.2 Periodic System: The Washboard Potential -- 2.5.3 Scaling -- 2.6 Timescales -- 2.6.1 Kramers Escape Times -- 2.7 Delay-Induced Oscillations and Coherence Resonance -- 2.7.1 Delay-Induced Oscillations -- 2.7.2 Coherence Resonance -- 2.7.3 Bifurcation Theoretical Perspective on Delay-Induced Oscillations -- References -- 3 Fokker-Planck Equations.
3.1 Markovian Case -- 3.1.1 Natural Boundary Conditions -- 3.1.2 Joint Probability Densities -- 3.1.3 The Probability Current and Steady States -- 3.2 Introduction to Fokker-Planck Descriptions of Systems with Time Delay -- 3.2.1 Earlier Approximation Schemes -- 3.2.2 Probability Current and Apparent Equilibrium of Time-Delayed Systems -- 3.2.3 Side Note: Delay in Ensemble-Averaged Quantities -- References -- 4 Stochastic Thermodynamics -- 4.1 Side Note: Some Historical Notes and Where Is Stochastic … -- 4.2 Stochastic Energetics -- 4.2.1 Steady States -- 4.3 Fluctuating Entropy -- 4.3.1 Thermal Equilibrium & -- Nonequilibrium Steady States -- 4.4 Fluctuation Theorems -- 4.4.1 Route to First Principles-Axiom of Causality -- 4.5 Information -- 4.5.1 Mutual Information and Its Generalization -- 4.5.2 Information Flow -- 4.6 Previous Results, Expectations and Apparent Problems for Systems with Time Delay -- 4.6.1 Energetics in the Presence of Delay -- 4.6.2 Entropic Description -- 4.6.3 The Acausality Issue -- 4.6.4 Short Comment on Effective Thermodynamics -- 4.7 Side Note: Active Particles & -- Non-reciprocal Interactions -- 4.7.1 Active Ornstein-Uhlenbeck Particles -- 4.7.2 Connection Between Active Matter and Time-Delayed Systems -- 4.7.3 Non-reciprocal Interactions -- References -- Part II Probabilistic Descriptions for Systems with Time Delay -- 5 Infinite Fokker-Planck Hierarchy -- 5.1 Derivation of Fokker-Planck Hierarchy from Novikov's Theorem -- 5.1.1 Alternative Approach with Two Time Arguments -- 5.2 Exact Probabilistic Solutions for Linear Systems with Time Delay -- 5.2.1 Derivation of the Second Member of the Fokker-Planck Hierarchy -- 5.2.2 Steady-State Solutions -- 5.2.3 The Notion of Effective Temperature -- 5.2.4 Markovian Versus Non-Markovian Two-Time Probability Density -- References. 6 Markovian Embedding-A New Derivation of the Fokker-Planck Hierarchy -- 6.1 Markovian Embedding-A Different View on Memory -- 6.1.1 Projection, Memory Kernel & -- Colored Noise -- 6.1.2 Limit ntoinfty -- 6.1.3 Interpretation of the Xj Variables -- 6.1.4 Initial Condition -- 6.1.5 (n+1)-dimensional Markovian Fokker-Planck Equation -- 6.2 Derivation of First Member of Fokker-Planck Hierarchy -- 6.3 Derivation of Higher Members via Markovian Embedding -- 6.3.1 Comparison to Equation from Novikov's Theorem -- 6.4 Side Note: Discrete Versus Distributed Delay -- 6.4.1 Distributed Delay -- 6.4.2 Probability Densities in the Presence of Discrete and Distributed Delay -- References -- 7 Force-Linearization Closure -- 7.1 Details of the Approximation -- 7.1.1 Linearization of the Deterministic Forces -- 7.1.2 Analytical Probabilistic Solution for Linearized Forces -- 7.1.3 Vanishing Steady-State Probability Current -- 7.1.4 Specification to Linear Delay Force -- 7.2 Comparison to Earlier Approaches -- 7.2.1 Small Delay Expansion -- 7.2.2 Perturbation Theory -- 7.2.3 Effective Temperatures -- 7.3 Application to the Periodic Potential -- 7.3.1 Discussion of Results -- 7.4 Application to the Bistable Potential -- 7.4.1 Discussion of Results -- 7.5 Estimation of Escape Times -- 7.5.1 Interwell Dynamics -- 7.5.2 The Kramers-FLC Estimate -- 7.5.3 Comparison with Numerical Results -- 7.5.4 Delay-Induced Oscillations -- 7.5.5 Side Note: Normal Diffusion Despite Non-Markovianity -- References -- 8 Approximation for the Two-time Probability density -- 8.1 Application to the Bistable Delayed System -- 8.1.1 Comparison with Approaches for One-time Probability Density -- 8.2 Concluding Remarks -- References -- Part III Thermodynamic Notions for Systems with Time Delay -- 9 The Heat Flow Induced by a Discrete Delay -- 9.1 Main Idea -- 9.1.1 Polynomial Energy Landscapes. 9.2 Mean Heat Rate & -- Medium Entropy Production -- 9.2.1 Linear Systems -- 9.2.2 Markovian Limits in Nonlinear Systems -- 9.2.3 Limit of Vanishing Delay Time -- 9.2.4 Influence of Inertia Term -- 9.2.5 Discussion of the Behavior for Small Delay Times -- 9.3 Application to the Bistable Potential -- 9.3.1 Low Thermal Energy-Intrawell Dynamics -- 9.3.2 High Thermal Energy-Interwell Dynamics -- 9.4 Preliminary Numerical Results for Fluctuation of Heat, Work and Internal Energy -- 9.5 Concluding Remarks -- References -- 10 Entropy, Information and Energy Flows -- 10.1 Emergence of Non-monotonic Memory -- 10.1.1 Interpretation of Xj> -- 0 in the Case of a Feedback Controller -- 10.2 The Role of Non-reciprocal Coupling-Connection to Active Matter -- 10.2.1 A Generic Model with Non-reciprocal Coupling -- 10.3 Non-reciprocal Coupling and Non-equilibrium -- 10.3.1 Fluctuation-Dissipation Relation -- 10.3.2 Total Entropy Production -- 10.3.3 Analytical Solutions -- 10.4 Non-reciprocal Coupling and Activity -- 10.4.1 Mapping Non-reciprocity of the Coupling to a Temperature Gradient Between the Coupled Entities -- 10.4.2 Reversed Heat Flow -- 10.5 Non-reciprocal Coupling and Information -- 10.5.1 Information Flow and Generalized Second Law -- 10.5.2 Information-Theoretic Perspective on Feedback Control -- 10.6 Total Entropy Production and Heat Flow in the Presence of Non-monotonic Memory -- 10.6.1 Limit of Discrete Delay -- 10.6.2 Impact of Measurement Errors -- 10.7 Irreversibility and Coarse-Graining -- References -- Part IV Concluding Remarks -- 11 Summary -- References -- 12 Outlook-Open Questions and Further Perspectives -- References -- Appendix Appendix -- A.1 Numerical Methods -- A.2 Derivation of Novikov's Theorem -- A.3 Green's Function Method -- A.4 Connection to Fokker-Planck Hierarchy from Novikov's Theorem. A.5 Fluctuation-Dissipation Relation for Unidirectional Ring of Arbitrary Length n -- Appendix About the Author. |
| Record Nr. | UNINA-9910502633203321 |
|
Loos Sarah A. M.
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Soggetto topico
-
Time delay systems
(14)
- Predictive control (3)
- Algebraic functions (2)
- Dynamics (2)
- Sistemes estocàstics (2)