Chaotic Dynamics

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insfProfessor: Dr. Hessein Nejat

Email: nejat@sharif.edu

Teacher Assistant: Ali Golzari

Email: golzariali93@yahoo.com

Syllabus

References

1. “Nonlinear Dynamics and Chaos”, Steven H.Strogatz, 2015

2. “Chaotic Vibration”, Francis C.Moon, 2014

Codes:

  1. Development of Different ODE Solvers: Cart and 2DOF Pendulum
  2. Subcritical PitchFork Bifurcation: Subcritical PitchFork Bifurication
  3. Insect Outbreak: Insect Outbreak
  4. Basin of attraction Basin of attraction
  5. Phase Portrait Display Phase Portrait Display
  6. Rabbit and Sheep Rabbit and Sheep
  7. Van der Pol Oscillator VAN DER POL OSCILLATOR
  8. Homoclinic Bifurcation: Homoclinic Bifurication
  9. Hysteresis in Pendulum Motion:Hysteresis in Pendulum Motion
  10. Lorenz System Analysis: Lorenz System Analysis
  11. Logistic Map: Logistic Map
  12. Von Koch Fractal: Von Koch
  13. Lorenz System Dimension: Lorenz System Dimension
  14. Logistic Map Dimension: Logistic Map Dimension
  15. Baker’s Map: Baker’s Map
  16. Henon Map: Henon Map
  17. Magneto Elastic Forced Beam: Magneto Elastic Forced Beam
  18. Rossler System: Rossler System

HW set 1: 2.2.13, 2.6.2, 2.8.2d

Deadline:  11 Mehr

 

HW set 2: Derive the equations of motion of a Two-D.O.F pendulum and solve it numerically using different numeric methods including Euler, Heun, Runge-Kutta (4, adaptive 4-5 Fehlberg, Adaptive Dormand_Prince, Ode45 MATLAB) and copare the results.

or problem 2.8.9

Deadline:  18 Mehr

 

HW set 3: 3.5.4, 3.6.5

Deadline:  25 Mehr

 

HW set 4: 4.3.3, 4.3.8, 5.2.14, 5.3.4

Deadline: 9 Aban

 

HW set 5: 6.3.9, 6.3.14, 6.5.17

Deadline: 16 Aban

 

HW set 6:  6.7.3, 6.8.7, 7.1.8, 7.2.12

Deadline: 23 Aban

 

HW set 7:  7.3.3, 7.4.2, 7.5.5, 7.6.9, 7.6.18

Deadline: 7 Azar

 

HW set 8:  8.1.6, 8.2.3, 8.2.12, 8.4.3

Deadline: 14 Azar

 

HW set 9:   8.5.2, 8.6.2, 8.7.9

Deadline: 26 Azar

 

HW set 10:   9.2.6, 9.3.5, 9.5.1, 9.5.4, 9.6.5

Deadline: 3 Dey

 

HW set 11:   10.1.11, 10.2.4, 10.3.2, 10.4.8, 10.5.6

Deadline: 14 Dey

 

HW set 12:   11.3.7, 11.3.8, 11.4.2, 11.5.2

Deadline: 21 Dey

 

HW set 13:   12.1.8, 12.2.7, 12.3.1, 12.5.2, 12.5.3, 12.5.4

Deadline: 28 Dey

 

HW set 14: 

Melnikov Problem: Melnikov Criteria

Deadline: Exam Day

سلام دانشجویان عزیز، نمرات اولیه شما بدون احتساب پروژه در سیستم edu وارد شده است. ریز نمرات Grades

در صورتیکه به نمره تمرین خود اعتراض دارید با مهندس گلذاری تماس بگیرید. امتحانات هم با دقت زیاد بررسی شده اند. البته در انتها  ارفاق شده است. در صورتیکه می خواهید برگه خود را ببینید امروز سه شنبه بین 6 تا 7 بعدازظهر مراجعه نمایید.

نمره پروژه به صورت مثبت حداکثر تا یک نمره به نمره فعلی شما اضافه خواهد شد.

برای پروژه ارائه نخواهیم داشت در عوض دانشجویان حداکثر تا پایان وقت چهارشنبه 11 بهمن فرصت ارسال گزارش نهایی خود را برای اینجانب و آقای مهندس گلذاری دارند. توجه فرمایید هنگام ارسال گزارش نهایی فایل مقاله یا مقالاتی که بر اساس آنها کار کردید را هم در یک فولدر زیپ نموده و ارسال نمایید.

Papers Recommended as Course Project:

  1. Miandoab, E. M., Pishkenari, H. N., Yousefi-Koma, A., & Tajaddodianfar, F. (2014). Chaos prediction in MEMS-NEMS resonators. International Journal of Engineering Science, 82, 74-83.
  2. Miandoab, E. M., Yousefi-Koma, A., Pishkenari, H. N., & Tajaddodianfar, F. (2015). Study of nonlinear dynamics and chaos in MEMS/NEMS resonators. Communications in Nonlinear Science and Numerical Simulation, 22(1), 611-622.
  3. Tajaddodianfar, F., Hairi Yazdi, M. R., & Pishkenari, H. N. (2015). On the chaotic vibrations of electrostatically actuated arch micro/nano resonators: a parametric study. International Journal of Bifurcation and Chaos, 25(08), 1550106.
  4. Tajaddodianfar, F., Pishkenari, H. N., & Yazdi, M. R. H. (2016). Prediction of chaos in electrostatically actuated arch micro-nano resonators: Analytical approach. Communications in Nonlinear Science and Numerical Simulation, 30(1), 182-195.
  5. Alemansour, H., Miandoab, E. M., & Pishkenari, H. N. (2017). Effect of size on the chaotic behavior of nano resonators. Communications in Nonlinear Science and Numerical Simulation, 44, 495-505.
  6. Pishkenari, H. N., Jalili, N., Mahboobi, S. H., Alasty, A., & Meghdari, A. (2010). Robust adaptive backstepping control of uncertain Lorenz system. Chaos: An Interdisciplinary Journal of Nonlinear Science, 20(2), 023105.
  7. Pishkenari, H. N., & Shahrokhi, M. (2005, January). Identification and Adaptive Control of the Uncertain Lorenz System. In ASME 2005 International Mechanical Engineering Congress and Exposition (pp. 1105-1111). American Society of Mechanical Engineers.
  8. Pishkenari, H. N., & Meghdari, A. (2008, May). Adaptive backstepping control of uncertain Lorenz system. In Mechatronics and Its Applications, 2008. ISMA 2008. 5th International Symposium on (pp. 1-6). IEEE.
  9. Mahboobi, S. H., Shahrokhi, M., & Pishkenari, H. N. (2006). Observer-based control design for three well-known chaotic systems. Chaos, Solitons & Fractals, 29(2), 381-392.
  10. Pishkenari, H. N., Shahrokhi, M., & Mahboobi, S. H. (2007). Adaptive regulation and set-point tracking of the Lorenz attractor. Chaos, Solitons & Fractals, 32(2), 832-846.
  11. Liang, X., & Qi, G. (2017). Mechanical analysis of Chen chaotic system. Chaos, Solitons & Fractals, 98, 173-177.
  12. Wang, H., & Tang, L. (2017). Modeling and experiment of bistable two-degree-of-freedom energy harvester with magnetic coupling. Mechanical Systems and Signal Processing, 86, 29-39.
  13. Foupouapouognigni, O., Buckjohn, C. N. D., Siewe, M. S., & Tchawoua, C. (2017). Nonlinear electromechanical energy harvesters with fractional inductance. Chaos, Solitons & Fractals, 103, 12-22.
  14. Kocamaz, U. E., Cevher, B., & Uyaroğlu, Y. (2017). Control and synchronization of chaos with sliding mode control based on cubic reaching rule. Chaos, Solitons & Fractals, 105, 92-98.
  15. Doroshin, A. V. (2017). Attitude dynamics of gyrostat–satellites under control by magnetic actuators at small perturbations. Communications in Nonlinear Science and Numerical Simulation, 49, 159-175.
  16. Krysko, A. V., Awrejcewicz, J., Pavlov, S. P., Zhigalov, M. V., & Krysko, V. A. (2017). Chaotic dynamics of the size-dependent non-linear micro-beam model. Communications in Nonlinear Science and Numerical Simulation, 50, 16-28.
  17. Lajimi, S. A. M., Heppler, G. R., & Abdel-Rahman, E. M. (2017). A parametric study of the nonlinear dynamics and sensitivity of a beam-rigid body microgyroscope. Communications in Nonlinear Science and Numerical Simulation, 50, 180-192.
  18. Petereit, J., & Pikovsky, A. (2017). Chaos synchronization by nonlinear coupling. Communications in Nonlinear Science and Numerical Simulation, 44, 344-351.
  19. Odibat, Z., Corson, N., Aziz-Alaoui, M. A., & Alsaedi, A. (2017). Chaos in Fractional Order Cubic Chua System and Synchronization. International Journal of Bifurcation and Chaos, 27(10), 1750161.

 

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