A Platform for Simulation and Analysis of Complex Systems

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Objective

The goal of this project is to design and develop a platform for simulating and analysing complex systems. Complex systems are characterised by emergent behaviour, meaning their long-term dynamics often cannot be fully understood through analytical methods alone. Instead, simulations are typically required to explore their behaviour over time. 

The software to be developed will allow users to:

  1. Define a “simple” nonlinear system (e.g., an equation in discrete time).
  2. Specify details about the system, such as parameter values, initial conditions, and simulation steps.
  3. Select the desired output format (e.g., numerical tables, identification of long-term behavior, visual diagrams representing system dynamics, etc.).
  4. Optionally, provide specific parameter values or define a range of values for parameter sweeps.

This platform will serve as a tool for exploring the behaviour of complex systems, enabling users to gain insights into their dynamics through both numerical and graphical representations.

Key Features

  1. System Input : Users can input a nonlinear system in a user-friendly format, such as a discrete-time equation.
  2. Parameter Specification : Allow users to define parameters, initial conditions, and simulation settings (e.g., time steps, ranges for parameter exploration).
  3. Simulation Execution : Perform simulations based on the provided inputs and generate outputs according to user preferences.
  4. Output Options : Provide multiple output formats, including:
    • Numerical tables with simulation results.
    • Identification of long-term behavior (e.g., convergence, oscillation, chaos).
    • Visual diagrams (e.g., trajectory plot, time evolution diagram, phase portraits, bifurcation diagrams).
  5. Parameter Sweeps : Enable users to simulate systems across a range of parameter values to study how changes affect system behavior.

Technology Stack

  • Programming Language : Python is suggested due to its versatility and rich ecosystem of libraries for scientific computing, data analysis, visualisation, and web development.
  • Software & Libraries :
    • The specific technology stack (e.g., frameworks, databases, front-end libraries) can be discussed with the instructor.
    • It is recommended that:
      • The presentation layer be web-based, ensuring accessibility and ease of use.
      • The application logic be implemented server-side to handle computationally intensive tasks securely and efficiently.

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