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The stream cipher based on a discrete piecewise linear chaotic map satisfies the security requirement of cipher design.
This Letter proposes a feedback controller, which is added to each chaotic map, such that the fixed point of the individual map satisfies the odd-number property.
Notice that identity map,, satisfies the condition (2.4).
Suppose that satisfies the partial KKM principle and a map satisfies the following.
Remark One can easily check that the Jacobian of a competitive map satisfies the sign structure.
That is, in addition to the cyclic condition, if the map satisfies the condition that for a given there exists a such that implies that.
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Such mapping satisfies the guidelines for performance-based design (PBD), which requires specification of two sets of spectral amplitudes one for which the structure will remain essentially linear, and the other for which it will undergo a nonlinear response.
where a mapping satisfies the condition.
Every nonexpansive mapping satisfies the condition.
If a mapping satisfies the inequality (2.1).
Suppose that the mapping satisfies the contractive condition (3.28).
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