1. Introduction to Dynamical Systems and Mathematical Preliminaries 

1. • Definition and basic concepts, Historical background and significance, Types of dynamical systems, Review of differential equations and difference equations, Basic calculus concepts (derivatives, integrals), Linear algebra essentials (matrices, eigenvalues, eigenvectors)

2. Stability Analysis 

1. • Linear stability analysis, Lyapunov stability theory, Center manifold theory, Stability analysis of periodic solutions and limit cycles

3. Phase-Space Analysis 

1. • Phase portraits, Equilibrium points and their classification, Reproduction number, Limit cycles and periodic solutions

4. Numerical Methods and simulation for Dynamical Systems 

1. • Euler's method, Runge-Kutta methods, Other numerical techniques for solving differential equations

   • Simulation and visualization of dynamical systems using software tools like MATLAB, Python, or Mathematica

5. Applications of Dynamical Systems 

1. • Applications in physics, biology, engineering, and social sciences, Case studies and real-world examples

   • Interdisciplinary perspectives on dynamical systems research

6. Advanced Topics in Dynamical Systems 

• • Nonlinear dynamics and chaos, Complex dynamical systems, Stochastic dynamical systems, Multi-scale and multi-agent systems

7. Advanced Methods in Dynamical Systems 

• Perturbation methods, Averaging methods, Normal forms, Hamiltonian systems and symplectic geometry

8. Chaos Theory 

• Chaos vs. randomness, Characteristics of chaotic systems, Chaos in discrete and continuous systems

9. Bifurcation theory

• Bifurcation Points, Types of Bifurcations 

10. Current Challenges and Future Directions 

• Open problems and unsolved questions in dynamical systems, Emerging trends and research frontiers

• Ethical considerations and responsible research practices in dynamical systems research, Recent advancements in dynamical systems research, Opportunities for interdisciplinary collaboration

The primary objective of this conference is to facilitate the convergence of academicians, researchers, and faculty members, providing them with a platform to exchange ideas, share experiences, and showcase research findings across diverse fields in dynamical systems. By bringing together professionals from academia and industry on a global scale, the FDP aims to foster collaboration and synergies that enhance the achievement of academic objectives. The associated Faculty Development Program (FDP) serves to equip researchers with insights into contemporary challenges, opportunities, and emerging trends in their respective fields, thereby ensuring their readiness to navigate and capitalize on the evolving academic landscape.