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As shown in the paper, thanks to the use of Dynamo architecture and the WebSocket protocol, on just one server node the state persistence system in Siebog can support thousands of external devices hosting tens of thousands of client-side agents, which is an excellent result.
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The main contributions of this article are as follows: (a) the existence of the global positive solution and the persistence of system (1.2) are discussed in detail; (b) the Hopf bifurcation analysis of system (1.2) is provided; (c) the Lyapunov function is constructed to complete the proof of global stability of the equilibria.
In order to prove the persistence of system (1.3) (see [27, Theorem 4.2]), we divided the proof process into two steps: Step 1, we show that system (1.3) is uniformly weakly ρ-persistent; Step 2, by the relative compactness of the orbit (Phi (t,(x_{i0},y_{i0}(cdot),v_{0}))), system (1.3) is uniformly strongly ρ-persistent.
Positivity of solutions and uniform persistence of system are studied.
Henry E. Smith, The Persistence of System in Property Law, 163 U. Pa.
persistence- Our system can run outdoors 24 hours a day 7, days a week collecting data the entire time with minimal interruptions.
Now, we will discuss extinction and persistence of system (1.3).
Second, we will give the persistence of system (1.3).
Remark 3.4 Theorem 3.1 gives the sufficient conditions for the uniform persistence of system (1.2).
The authors showed the asymptotic smoothness of solutions and uniform persistence of system (1.1).
In what follows, we will discuss the extinction and persistence of system (1.1).
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