Mathematical Problems for Complex Systems

As most of practical systems have high complexity, complex systems have become a rapidly growing area of mathematics and attracted many researchers. The study of complex systems not only has an important theoretical interest but also is motivated by problems from applied mathematics including physics, chemistry, astronomy, technology, and natural and social sciences. It should be noted that some major problems have not been fully investigated, such as the behavior of stability, synchronization, bifurcation, and chaos control for complex systems, as well as their applications in, for example, communication and bioinformatics. The special issue contains seven papers; of these, three of the papers are related to application analysis of complex systems to the real world problems. One paper studies the synchronization of chaotic complex systems with fractional-order. One paper investigates the consensus problem for non-linear complex systems. Another paper provides an approach to determine the unique 3-uniform linear hypertree with the maximum Estrada index. Finally, a paper provides interior principles to calculate the leading elements of the aliased effect-number pattern. In the paper " Results for Two-Level Designs with General Minimum Lower-Order Confounding, " the authors study the interior principles of calculating the leading elements in # 1 í µí° ¶ 1 and # 2 í µí° ¶ 2 aliased effect-number pattern. Also, their mathematical formulations are obtained for every lower-order confounding 2 í µí±›−í µí±š design according to the two different cases. In the paper " On the Maximum Estrada Index of 3-Uniform Linear Hypertrees, " authors give some basic definitions on the Estrada index of hypergraph and then formulate an algorism for determining the unique 3-uniform linear hypertree with the maximum Estrada index. In the paper " Consensus of Nonlinear Complex Systems with Edge Betweenness Centrality Measure under Time-Varying Sampled-Data Protocol, " by constructing a suitable Lyapunov-Krasovskii functional and using linear matrix inequality technique, the authors propose a new consensus criterion for nonlinear complex systems with edge betweenness centrality measure. Finally, a numerical example is provided to illustrate the effectiveness of the proposed consensus schemes. In the paper " One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1 < í µí±ž < 2, " based on a new stability result of equilibrium point in nonlinear fractional-order systems, the authors investigate the adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < í µí±ž < 2. Numerical simulations show the feasibility of the proposed adaptive …