Non‐instantaneous impulsive stochastic FitzHugh–Nagumo equation with fractional Brownian motion

DOI10.1002/mma.9076zbMath1529.60044OpenAlexW4319828473MaRDI QIDQ6179910

Muslim Malik, Nagarajan Durga

Publication date: 18 December 2023

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.9076

zbMATH Keywords

exponential stabilityfractional Brownian motionexistence of solutionnon-instantaneous impulseFitzHugh-Nagumo equation

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Brownian motion (60J65) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Cites Work

• Unnamed Item
• Decay mild solutions for two-term time fractional differential equations in Banach spaces
• Neutral stochastic functional differential equations driven by a fractional Brownian motion in a Hilbert space
• Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability
• Existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fBm with noncompact semigroup via Mönch fixed point
• Existence and exponential behavior of multi-valued nonlinear fractional stochastic integro-differential equations with Poisson jumps of Clarke's subdifferential type
• Continuity and random dynamics of the non-autonomous stochastic FitzHugh-Nagumo system on \(\mathbb{R}^N\)
• Stability analysis for discrete time abstract fractional differential equations
• Stochastic dynamics of the FitzHugh-Nagumo neuron model through a modified van der Pol equation with fractional-order term and Gaussian white noise excitation
• Ergodicity and spike rate for stochastic FitzHugh-Nagumo neural model with periodic forcing
• Optimal control of the FitzHugh-Nagumo stochastic model with nonlinear diffusion
• Patterns of interaction of coupled reaction-diffusion systems of the Fitzhugh-Nagumo type
• The stochastic FitzHugh-Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model
• Smoothing dynamics of the non-autonomous stochastic Fitzhugh-Nagumo system on \(\mathbb{R}^N\) driven by multiplicative noises
• Effects of Lévy noise on the Fitzhugh-Nagumo model: a perspective on the maximal likely trajectories
• Stability analysis for nonlinear fractional-order systems based on comparison principle
• Optimal control of stochastic FitzHugh–Nagumo equation
• Mixed fractional stochastic differential equations with jumps
• Stochastic time-optimal control for time-fractional Ginzburg–Landau equation with mixed fractional Brownian motion
• ANALYSIS OF THE STOCHASTIC FITZHUGH–NAGUMO SYSTEM
• Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces
• On a new class of abstract impulsive differential equations
• Non-instantaneous impulsive Hilfer fractional stochastic differential equations driven by fractional Brownian motion
• On stability of stochastic differential equations with random impulses driven by Poisson jumps
• Existence, stability and controllability results of stochastic differential equations with non-instantaneous impulses
• Wong-Zakai approximations and attractors for non-autonomous stochastic FitzHugh-Nagumo system on unbounded domains
• Optimal controls for second‐order stochastic differential equations driven by mixed‐fractional Brownian motion with impulses
• Approximate controllability of semilinear retarded stochastic differential system with non-instantaneous impulses: Fredholm theory approach
• Fractional Brownian Motions, Fractional Noises and Applications