Lotka-Volterra systems with retarded argument

Introduction
Ch.1. Preliminaries
1.1. Process of mathematical modeling
1.1.1. Lotka-Volterra model
1.1.2. Lotka-Volterra model with delay
1.2. Systems of differential equations with  retarded argument
1.3. Theorems  of fixed point on metric spaces
1.4. Weakly Picard operators on metric spaces
1.5. Spline functions

Ch.2. Existence and uniqueness theorems and date dependence
2.1. Formulation of the problem
2.2. Step method
2.3. Existence and uniqueness
2.4. Comparison theorems
2.5. Continuous dependence with respect to the dates of the problems
2.6. Data dependence of the fixed point set
2.7. Examples
2.8. Remarks and generalizations

Ch.3. Differentiability with respect to parameters
3.1. Formulation of the problem
3.2. Continuous differentiability with respect to parameters
3.3. Continuous differentiability with respect to delays
3.4. Differentiability with respect to parameters via step method
3.5. Examples

Ch.4 Methods of approximation for the solution
4.1. The quadratures formula techniques
4.1.1. The quadratures formula techniques
4.1.2. Formulation of the problem
4.1.3. The numerical of the integral from the succesive approximation
4.1.4. The approximation of the succesive approximation sequences
4.2. Spline functions techniques
4.2.1. Numerical solutions with spline functions of even degree
4.2.3. Examples

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