In this study, a discrete fractional Henon map is proposed in the Caputo discrete delta's sense. The results show that the discrete fractional calculus is an efficient tool and the maps derived in this way have simpler forms but hold rich dynamical behaviors.
In this paper, we theoretically and numerically investigate anti-synchronization between two weighted dynamical networks. Based on the Barbalat lemma, we propose two adaptive controllers to realize the global anti-synchronization between two networks with both equivalent and different topological structures. In addition, we derive two theorems on the anti-synchronization based on the Lyapunov stability theory and verify them by extensive numerical examples.
In this paper, we study a nonlinear third-order multipoint boundary value problem by the monotone iterative method. We then obtain the existence of monotone positive solutions and establish iterative schemes for approximating the solutions. In addition, we extend the considered problem to the Riemann-Liouville-type fractional analogue. Finally, we give a numerical example for demonstrating the efficiency of the theoretical results.
In this paper, the leaderless coherence and leader–follower coherence defined by the Laplacian spectrum are applied to noisy trees with given parameters. The asymmetry of the trees is controlled by the degrees of hub nodes. Based on the tree’s structures, analytical solutions are obtained for these two types of consensus algorithms. In order to compare the leaderless and leader–follower coherence, two trees with the same network size are selected and then explicit expressions of the coherence are given. Obtained results reveal that bigger difference of the degrees of the hubs leads to higher coherence and the consensus of a tree without a leader becomes better. Finally, it is found that the leader–follower coherence changes higher with more leaders and larger network parameters.
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