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Integral Manifolds for Impulsive Differential Problems with Applications
- 1st Edition - May 1, 2025
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 3 0 1 3 4 - 6
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 3 0 1 3 5 - 3
Integral Manifolds for Impulsive Differential Problems with Applications offers readers a comprehensive resource on integral manifolds for different classes of differential equati… Read more
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Request a sales quoteIntegral Manifolds for Impulsive Differential Problems with Applications offers readers a comprehensive resource on integral manifolds for different classes of differential equations which will be of prime importance to researchers in applied mathematics, engineering, and physics. The book offers a highly application-oriented approach, reviewing the qualitative properties of integral manifolds which have significant practical applications in emerging areas such as optimal control, biology, mechanics, medicine, biotechnologies, electronics, and economics. For applied scientists, this will be an important introduction to the qualitative theory of impulsive and fractional equations which will be key in their initial steps towards adopting results and methods in their research.
- Offers a comprehensive resource of qualitative results for integral manifolds related to different classes of impulsive differential equations, delayed differential equations and fractional differential equations
- Presents the manifestations of different constructive methods, by demonstrating how these effective techniques can be applied to investigate qualitative properties of integral manifolds
- Discusses applications to neural networks, fractional biological models, models in population dynamics, and models in economics of diverse fields
Graduate students, researchers, and professionals in applied mathematics, engineering, and physics for whom integral manifolds approaches are important tools to study the qualitative properties of different classes of dynamical systems, including impulsive differential equations and equations that follow fractional-order dynamics
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
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
- No. of pages: 300
- Language: English
- Edition: 1
- Published: May 1, 2025
- Imprint: Academic Press
- Paperback ISBN: 9780443301346
- eBook ISBN: 9780443301353