Integral Manifolds for Impulsive Differential Problems with Applications

1: Basic Theory


2: Integral Manifolds and Impulsive Differential Equations

2.1. Integral Manifolds and Impulsive Differential Equations

2.1.1. Integral Manifolds and Perturbations of the Linear Part of Impulsive Differential Equations

2.1.2. Integral Manifolds and Singularly Perturbed Impulsive Differential Equations

2.2. Affinity Integral Manifolds for Linear Singularly Perturbed Systems of Impulsive Differential Equations

2.3. Integral Manifolds of Impulsive Differential Equations Defined on Torus


3. Impulsive Differential Systems and Stability of Manifolds

3.1. Stability of Integral Manifolds

3.1.1. Integral Manifolds and Principle of the Reduction for Impulsive Differential Equations

3.1.2 Integral Manifolds and Principle of the Reduction for Singularly Impulsive Differential Equations

3.1.3. Integral Manifolds and Boundedness of the Solutions of Impulsive Functional Differential Equations

3.1.4. Integral Manifolds and Asymptotic Stability of Sets for Impulsive Functional Differential Equations

3.2. Stability of Moving Integral Manifolds

3.2.1. Stability of Moving Integral Manifolds for Impulsive Differential Equations

3.2.2. Stability of Moving Conditionally Integral Manifolds for Impulsive Differential Equations

3.2.3. Stability of Moving Integral Manifolds for Impulsive Integro-Differential Equations

3.2.4. Stability of Moving Integral Manifolds for Impulsive Differential-Difference Equations

3.3. Stability of H-Manifolds

3.3.1. Practical Stability with Respect to h-Manifolds for Impulsive Functional Differential Equations with Variable Impulsive Perturbations

3.3.2 Impulsive Control Functional Differential Systems of Fractional Order: Stability with Respect to h-Manifolds


4. Applications

4.1. Integral Manifolds and Impulsive Neural Networks

4.1.1. Integral Manifolds and Impulsive Neural Networks with Time-varying Delays

4.1.2. Stability with Respect to H-manifolds of Cohen-Grossberg Neural Networks with Time-varying Delay and Variable Impulsive Perturbations

4.2. Integral Manifolds and Mathematical Models in Biology

4.2.1. Integral Manifolds and Kolmogorov Systems of Fractional Impulsive Differential Equations

4.2.2. Impulsive Lasota-Wazewska Equations of Fractional Order with Time-varying Delays: Integral Manifolds

4.3. Solow-type Models and Stability with respect to Manifolds

4.4 Reaction-Diffusion Impulsive Neural Networks and Stability with Respect to Manifolds

4.4.1. Stability of Sets Criteria for Impulsive Cohen –Grossberg Delayed Neural Networks with Reaction –Diffusion Terms

4.4.2. Global Stability of Integral Manifolds for Reaction –Diffusion Cohen–Grossberg-type Delayed Neural Networks with Variable Impulsive Perturbations

4.4.3. Impulsive Reaction-Diffusion Delayed Models in Biology: Integral Manifolds Approach

4.4.4. h-Manifolds Stability for Impulsive Delayed SIR Epidemic Model

4.4.5 Impulsive Control of Reaction-Diffusion Impulsive Fractional Order Neural Networks with Time-varying Delays and Stability with Respect to Integral Manifolds

4.4.6. Reaction-Diffusion Impulsive Fractional-order Bidirectional Neural Networks with Distributed Delays: Mittag-Leffler Stability along Manifolds