Almost Sure and Moment Exponential Stability of Regime-Switching Jump Diffusions

Chao, Zhen; Wang, Kai; Zhu, Chao; Zhu, Yanling

doi:10.1137/16m1082470

Cited by 26 publications

(10 citation statements)

References 35 publications

(81 reference statements)

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“…Remark As a non‐Gaussian noise with heavy tails and jumps, Lévy noise exists widely in natural environment. It has been found in neural networks, signal processing, disease spreading, heartbeat dynamics, and so on 23,24,26 . We take an example of neural network to verify that there exists Lévy noise in coupled systems in science and engineering 33 .…”

Section: Preliminaries and Model Formulationmentioning

confidence: 98%

“…It has been found in neural networks, signal processing, disease spreading, heartbeat dynamics, and so on. 23,24,26 We take an example of neural network to verify that there exists Lévy noise in coupled systems in science and engineering. 33 Recently, the artificial neural network has been widely applied in theoretical and practical fields.…”

Section: Preliminaries and Model Formulationmentioning

confidence: 99%

“…Definition 26 Assuming

V_{i} \in C^{2, 1} false(ℝ^{\overset{m}{true}} \times ℝ_{+}^{1} \times 𝕊; ℝ_{+}^{1} false)

, and

k \in 𝕊

, the operator

scriptL V_{i}

from

ℝ^{\overset{m}{true}} \times ℝ_{+}^{1} \times 𝕊

ℝ^{1}

with regard to the i ‐th subsystem of system () is defined as follows:

\begin{matrix} scriptL V_{i} false(e_{i}, t, k false) = & \frac{\partial V_{i} false(e_{i}, t, k false)}{\partial t} + \frac{\partial V_{i} false(e_{i}, t, k false)}{\partial e_{i}} ([], u_{i} false(t false) + {\overset{α}{true}}_{i} + true \sum_{j = 1}^{n} a_{i j}^{false(1 false)} false(k false) δ_{i j}) \\ + \frac{1}{2} Tr ([], {((), {\overset{β}{true}}_{i} + true \sum_{j = 1}^{n} a_{i j}^{false(2 false)} false(k false) η_{i j})}^{normalT} \partial^{2} V_{i} false(e) \end{matrix}

…”

Section: Preliminaries and Model Formulationmentioning

confidence: 99%

“…That is, Lévy noise is well known to incorporate both small and big jumps, whereas Markovian switching provides the qualitative changes of the environment. 26 In brief, Markovian switching and Lévy noise provide a uniform and realistic yet mathematically tractable platform in modeling a wide range of applications. Consequently, to describe the actual features of SDCN, the realistic modeling of many networks is necessary to take Markovian switching and Lévy noise into account, despite their increasing mathematical complexity.…”

Section: Introductionmentioning

confidence: 99%

“…Markovian switching and Lévy noise naturally captures these inherent features of these systems. That is, Lévy noise is well known to incorporate both small and big jumps, whereas Markovian switching provides the qualitative changes of the environment 26 . In brief, Markovian switching and Lévy noise provide a uniform and realistic yet mathematically tractable platform in modeling a wide range of applications.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization for stochastic hybrid coupled controlled systems with Lévy noise

Zhou

2020

Math Methods in App Sciences

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In this paper, synchronization for stochastic hybrid-delayed coupled systems with Lévy noise on a network (SHDCLN) is investigated via aperiodically intermittent control. Here time delays, Markovian switching and Lévy noise are considered on a network simultaneously for the first time. After that, by means of Lyapunov method, graph theory, and some techniques of inequality, some sufficient conditions are derived to guarantee the synchronization for SHDCLN. In addition, the designed range of aperiodically intermittent controller parameters is shown. Meanwhile, the coupling strength and the perturbed intensity of noise have a great impact on the intensity of control. Then, we investigate synchronization for stochastic hybrid delayed Chua's circuits with Lévy noise on a network as a practical application of our theoretical results. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

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