Dynamical Systems Modeling and Analysis

11.

Applications in Biology

11.1.

Population Dynamics

11.1.1.

Single Species Models

11.1.1.1.

Exponential Growth

11.1.1.2.

Logistic Growth

11.1.1.3.

11.1.2.

Predator-Prey Systems

11.1.2.1.

Lotka-Volterra Model

11.1.2.2.

Modifications and Extensions

11.1.2.3.

Stability Analysis

11.1.3.

Competition Models

11.1.3.1.

Competitive Exclusion

11.1.3.2.

Coexistence Conditions

11.1.4.

Metapopulation Models

11.1.4.1.

11.1.4.2.

Migration Effects

11.2.

11.2.1.

11.2.1.1.

Basic Reproduction Number

11.2.1.2.

Epidemic Thresholds

11.2.1.3.

Vaccination Strategies

11.2.2.

11.2.2.1.

Latent Period Effects

11.2.2.2.

Disease Progression

11.2.3.

Spatial Spread Models

11.2.3.1.

Reaction-Diffusion Equations

11.2.3.2.

Traveling Waves

11.3.

11.3.1.

Single Neuron Models

11.3.1.1.

Integrate-and-Fire Model

11.3.1.2.

Hodgkin-Huxley Model

11.3.1.3.

FitzHugh-Nagumo Model

11.3.2.

Neural Networks

11.3.2.1.

Coupled Oscillators

11.3.2.2.

Synchronization

11.3.2.3.

Network Dynamics

11.4.

11.4.1.

Food Web Dynamics

11.4.2.

Ecosystem Stability

11.4.3.

Spatial Patterns

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