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For rapid construction and simulation of CMLs

Getting Started

  1. Coupling scheme
  2. Map function
  3. CML object
  4. Evolution and Analysis

Coupling Schemes

Each coupling scheme requires a couple() function:

  • input: the lattice in its previous state
  • output: the lattice in its updated state This may require sub-functions. For example,

Two-Neighbor Coupling

\[ x_{n+1}(i) = (1 - \epsilon)f(x_{n}(i)) + \frac{\epsilon}{2}(f(x_{n}(i + 1)) + f(x_{n}(i - 1))) \] +++?code=couplings.py&title=Implementation @[7](Classic two-neighbor coupling scheme) @[8-10](Requires a coupling strength and a Map object) @[11]((Which determines the map function used)) @[19-33](The overarching coupling function) @[13-14](Delegate function for updating lattice boundaries) @[16-17](Delegate function for updating internal lattice cells)

Map Functions

Each map requires a _map() function:

  • input: a previous state
  • output: the next state and parameter(s) alpha

Kaneko Logistic Map

\[ f(x) = 1 - \alpha x^{2} \] +++?code=maps.py&title=Implementation @[5-11](General Map class) @[8-11](Bifurcation Parameter getter/setters) @[19-23](Kaneko logistic map class) @[22-23](Map function updates previous state)