Material para complementar as aulas de dinâmica não-linear.

Plots de diagramas de bifurcação

• Transcritica - Mathematica / Geogebra
• Supercritical Pitchfork - Mathematica / Geogebra
• Supercritical Pitchfork Catastrophe - Mathematica / Geogebra
• Subcritical Pitchfork - Mathematica / Geogebra
• Saddle-Node - Mathematica / Geogebra
• Subcritical Pitchfork + Saddle-Node - Geogebra
• Sel'kov model with Hopf bifurcation

Slides das aulas

1. https://www.dropbox.com/scl/fi/981zrhsr20tm6blnyb2ma/aula1_minicurso_pos.pptx?rlkey=0ds5oigumt3r1nmtbd4gtpmao&dl=0
2. https://www.dropbox.com/scl/fi/6b40rtzs8291kfa31eoa9/aula2_minicurso_pos.pptx?rlkey=oq6mikuo0p4a5vfw1himjuond&dl=0
3. https://www.dropbox.com/scl/fi/9n0ob6ziqdnwrtntebp73/aula3_minicurso_pos.pptx?rlkey=vof5cj8dosrrojjp8supftlwm&dl=0

Bibliografia

1. Strogatz, S. (2015) Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering. Westview Press
2. Abraham & Shaw 1992. Dynamics: the geometry of behavior. 2nd ed. Addison Wesley
3. Monteiro LHA (2023) Sistemas Dinâmicos 4a ed. Livraria da Física
4. Izhikevich E.M. (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. The MIT press
5. Y. Kuznetsov (2004) Elements of Applied Bifurcation Theory. Springer

Artigos

7. Girardi-Schappo M et al. (2017) Phase diagrams and dynamics of a computationally efficient map-based neuron model. PLoS ONE 12: e0174621. https://doi.org/10.1371/journal.pone.0174621
8. Girardi-Schappo M et al. (2021) A unified theory of E/I synaptic balance, quasicritical neuronal avalanches and asynchronous irregular spiking. J. Phys. Complex. 2 045001. https://doi.org/10.1088/2632-072X/ac2792