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Later, in a morphological study combining cytogenetical and ecological data when available, Delabie et al. [59] demonstrated that, given the stability of differences through multiple cases of sympatry, the variability pointed by Wild [54] could in fact refer to a species mosaic rather than a geographic cline.
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Similarly, we present the stability of difference scheme (2.7)–(2.7).
In applications, the stability of difference schemes for elliptic differential equations is presented.
In Section 2, theorems on coercive stability of difference schemes (9) and (10) are established.
Below, we consider a similar approach for studying the stability of difference systems with delay.
Now, we will give the first main theorem of the present paper on the stability of difference scheme (2).
Particularly, the study of asymptotic stability of numerical schemes (including construction of stability regions) is based on the results for asymptotic stability of difference equations.
We prove two new criteria for the sufficiency of the von Neumann condition for stability of difference schemes.
Further, by constructing discrete type Lyapunov functions and using the theory of stability of difference equations, we establish the global asymptotic stability of the equilibria.
Therefore, using the theorems of stability of difference equations, we finally obtain that the endemic equilibrium (P_) of model (12) is globally attractive.
The following examples show the advantages of Theorems 3.1 over Theorem A in analyzing the Schur stability of difference equations (discrete-time systems).
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