Under such a setting, we derive the synchronization mechanism for rotation and scaling as follows.
By exploiting the characteristics of shift-invariance, steerability, and scalability, we further derived the theoretical synchronization mechanisms for translation, rotation, and scaling.
Individual connectivity differences derived for the synchronization changes are represented at 3 superior-to-inferior levels through the brain shown in Figure 4 (b d).
In Section 4, we theoretically derive the RST synchronization mechanism.
In what follows, we will design appropriate control schemes to derive the projective synchronization conditions between systems (10) and (11).
By the proof of Theorem 2, we can derive the exponential synchronization criteria of the network (1) with the fixed impulsive gain, which is given as follows.
If the switching signal σ ( t ) ≡ 1, then the network (1) has only one coupling matrix G. Suppose G is irreducible and ξ T = ( ξ 1, ξ 2, …, ξ N ) is the left eigenvector of coupling matrix G corresponding to eigenvalue 0. By the proof of Theorem 1, we can derive the exponential synchronization criteria of the network (1) with only one topology, which is given as follows.
In this paper, based on the derived RST synchronization mechanism, we develop a new robust image watermarking that is resilient to RST.
The properties of the Hill equation and the Whittaker method are used to derive the stability conditions of the synchronization process.
By constructing suitable Lyapunov function and using the presented lemma, some sufficient criteria are derived to achieve the synchronization of fractional order complex-variable dynamical networks under the corresponding update law.
