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Method of analysis: Discrete map iteration and Lyapunov exponent calculation. Behavior description: Iterative process that can produce a fractal structure known as the Henon attractor.

Method of analysis: Numerical simulation and bifurcation analysis. Behavior description: Exhibits chaotic behavior and resembles the structure of a twisted band.

Method of analysis: Phase plane analysis and numerical computation. Behavior description: Self-sustained oscillations and limit cycle behavior.

Method of analysis: Numerical simulation and circuit analysis. Behavior description: Known to produce a variety of complex dynamical behaviors including chaotic oscillations.

Method of analysis: Numerical simulation and qualitative analysis. Behavior description: Sensitive dependence on initial conditions leading to what is known as the 'butterfly effect'.

Method of analysis: Hamiltonian mechanics and numerical simulation. Behavior description: Highly sensitive to initial conditions and can display chaotic motion.