Integral Manifolds for Impulsive Differential Problems with Applications

1. Basic theory
1.1 Introduction
1.2 Impulsive differential equations
1.2.1 Impulsive ordinary differential equations with variable impulsive perturbations
1.2.2 Impulsive ordinary differential equations with fixed moments of impulsive perturbations
1.3 Impulsive functional differential equations
1.4 Impulsive fractional differential equations
1.5 Impulsive conformable differential equations
1.6 Integral manifolds
1.7 Lyapunov method and impulsive differential equations
1.7.1 Piecewise continuous Lyapunov functions
1.7.2 Lyapunov-Razumikhin method
1.7.3 Fractional Lyapunov function method
1.7.4 Conformable Lyapunov function method
1.8 Comparison results
1.9 Notes and comments

2. Impulsive differential equations and existence of integral manifolds
2.1 Integral manifolds for impulsive differential equations
2.1.1 Integral manifolds for impulsive functional differential equations
2.1.2 Integral manifolds for impulsive uncertain functional differential equations
2.1.3 Integral manifolds for impulsive fractional functional differential equations
2.2 Impulsive differential equations and (?, ?)-integral manifolds
2.2.1 Integral manifolds of (?, ?)-type and perturbations of the linear part of impulsive differential equations
2.2.2 (?, ?)-integral manifolds for singularly perturbed impulsive differential equations
2.3 Affinity integral manifolds for linear singularly perturbed systems of impulsive differential equations
2.4 Integral manifolds of impulsive differential equations defined on a torus
2.5 Notes and comments

3. Impulsive differential equations and stability of integral manifolds
3.1 Lyapunov method and stability of integral manifolds
3.2 Stability of moving integral manifolds
3.2.1 Stability of moving integral manifolds for impulsive ordinary differential equations
3.2.2 Stability of conditionally moving integral manifolds for impulsive ordinary differential equations
3.2.3 Stability of moving integral manifolds for impulsive functional differential equations
3.3 Stability with respect to h-manifolds
3.3.1 Practical stability with respect to h-manifolds for impulsive functional differential equations with variable impulsive perturbations
3.3.2 Stability with respect to h-manifolds for impulsive functional differential systems of fractional order
3.3.3 Practical stability with respect to h-manifolds for impulsive conformable differential equations
3.4 Reduction principle and stability of integral manifolds
3.4.1 Integral manifolds and the reduction principle for impulsive differential equations
3.4.2 Integral manifolds and the reduction principle for singularly perturbed impulsive differential equations
3.5 Notes and comments

4. Applications: integral manifolds and impulsive differential models
4.1 Impulsive neural networks and integral manifolds
4.1.1 Integral manifolds for impulsive cellular neural networks
4.1.2 Stability with respect to h-manifolds of impulsive Cohen-Grossberg neural networks
4.1.3 Integral manifolds for impulsive reaction-diffusion neural networks
4.2 Integral manifolds for impulsive models in biology and medicine
4.2.1 Stable manifolds for impulsive Lotka-Volterra models
4.2.2 Integral manifolds for impulsive Lasota-Wazewska models
4.2.3 Integral manifolds for impulsive epidemic and virus dynamic models
4.2.4 Integral manifolds for impulsive Kolmogorov models
4.3 Integral manifolds for impulsive models in finance
4.4 Notes and comments
References
Index