![]() Section 2. Section 2.3: Maths is one thing, but neuroscience matters Interactive Demo 2.2: The Impact of Input ![]() Interactive Demo 2.1.1: Initial Condition Section 2.1.1: Exact Solution of the LIF model without input Video 3: The leaky integrate and fire model Section 2: The leaky integrate and fire model Interactive Demo 1.2: Interactive Parameter Change Go to this website to explore more on this topic. A solution to a differential equation is a function y f(x) that satisfies the differential equation when f and its derivatives are substituted into the equation. Section 1.2: Parameters of the differential equation A differential equation is an equation involving an unknown function y f(x) and one or more of its derivatives. Section 1.1: Exact solution of the population equationĮxample Exact Solution of the Population Equation Think! 1.1: Interpretating the behavior of a linear population equation Video 2: Population differential equation Section 1: Population differential equation Video 1: Why do we care about differential equations? Tutorial 3: Simultaneous fitting/regressionĮxample Model Project: the Train Illusion Tutorial 4: Model-Based Reinforcement Learning Tutorial 2: Learning to Act: Multi-Armed Bandits Tutorial 2: Optimal Control for Continuous State Tutorial 1: Optimal Control for Discrete States Tutorial 1: Sequential Probability Ratio Testīonus Tutorial 4: The Kalman Filter, part 2īonus Tutorial 5: Expectation Maximization for spiking neurons Tutorial 2: Bayesian inference and decisions with continuous hidden state Tutorial 1: Bayes with a binary hidden state Tutorial 3: Synaptic transmission - Models of static and dynamic synapsesīonus Tutorial: Spike-timing dependent plasticity (STDP)īonus Tutorial: Extending the Wilson-Cowan Model ![]() Tutorial 1: The Leaky Integrate-and-Fire (LIF) Neuron Model Tutorial 3: Combining determinism and stochasticity Tutorial 3: Building and Evaluating Normative Encoding Modelsīonus Tutorial: Diving Deeper into Decoding & Encoding Tutorial 2: Convolutional Neural Networks Tutorial 4: Nonlinear Dimensionality Reduction Tutorial 3: Dimensionality Reduction & Reconstruction Tutorial 6: Model Selection: Cross-validation Tutorial 5: Model Selection: Bias-variance trade-off Tutorial 4: Multiple linear regression and polynomial regression Tutorial 3: Confidence intervals and bootstrapping Find all equilibrium solutions of Equation 9.4.1 and classify them as stable or unstable. Sketch a slope field below as well as a few typical solutions on the axes provided. (The Lotka-Volterra model of population dynamics). We will look at the standard Lotka-Volterra model in this section. In the predator-prey model, one typically has one species, the predator, feeding on the other, the prey. We begin with the differential equation (9.4.1) d P d t 1 2 P. Two well-known nonlinear population models are the predator-prey and competing species models. Tutorial 1: Differentiation and Integration Recall that one model for population growth states that a population grows at a rate proportional to its size. Prerequisites and preparatory materials for NMA Computational Neuroscienceīonus Tutorial: Discrete Dynamical Systems In this section, we would like to find $y(t)$ for the interval $$ that we divide into $N+1$ equally-spaced points $t_0< t_1 <. Numerical methods for ODE - Initial value problems Let N(t) be the population at time t and Let N0 denote the initial population, that is, N(0)N0. Remark: If the condition does not apply, then we cannot say anything about uniqueness. Bernoulli, $n\in\mathbb(x,y)$ are continuous at all points in a rectangular region containing $(x_0,y_0)$, then $y'=f(x,y)$ has a unique solution $y(x)$ passing through $(x_0,y_0)$.
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