Institute for Computational Neuroscience

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Quasiperiodicity and Mode Locking in The Circle Map & Effect of Noise on The Period Doubling Transition to Chaos in The Stochastic Systems.

In the first part of our seminar, we will investigate the quasiperiodicity, mode locking and bifurcation structure in the circle map. In the second part, we will study the effect of noise on the period doubling transition to chaos in the stochastic dynamical systems.

1. Quasiperiodicity and mode locking in the circle map (Jul. 20.). [ PPT ]

2. Effect of noise on the period doubling transition to chaos in the stochastic dynamical systems.

2.1. Stochastic 1D map.

a. Scaling behaviors in the stochastic 1D map (Jul. 27).

b. Confirmation of the scaling behaviors in the stochastic 1D map (Aug. 3.).

2.2. Stochastic ordinary differential equation (ODE).

a. Solving the stochastic ODE (Aug. 10.).

b. Effect of noise on the period doubling transition to chaos in the stochastic ODE (Aug. 17.).

Final Report

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