Complex and Fractional Dynamics

Complex systems (CS) are pervasive in many areas, namely financial markets; highway transportation; telecommunication networks; world and country economies; social networks; immunological systems; living organisms; computational systems; and electrical and mechanical structures. CS are often composed of a large number of interconnected and interacting entities exhibiting much richer global scale dynamics than could be inferred from the properties and behavior of individual elements. This Special Issue focuses on the topics of complex dynamical systems, nonlinearity, chaos and fractional dynamics, from the perspectives of both thermodynamics and information processing. This selection of 21 papers addressing advanced issues and specific topics illustrates the broad impact of entropy-based techniques in complexity, nonlinearity and fractionality. In the paper A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization, Shibing Wang, Xingyuan Wang and Yufei Zhou introduce a novel complex Lorenz system with a flux-controlled memristor, investigating its synchronization [1]. The manuscript A Novel Image Encryption Algorithm Based on DNA Encoding and Spatiotemporal Chaos, by Chunyan Song and Yulong Qiao, proposes a novel image encryption scheme based on DNA encoding and spatiotemporal chaos [2]. In the work A Novel Weak Fuzzy Solution for Fuzzy Linear System, Soheil Salahshour, Ali Ahmadian, Fudziah Ismail and Dumitru Baleanu propose a novel weak fuzzy solution for the fuzzy linear system. Two complex and non-complex linear systems under uncertainty are tested to validate the effectiveness and correctness of the method [3]. In the article Adaptive Synchronization for a Class of Uncertain Fractional-Order Neural Networks, Heng Liu, Shenggang Li, Hongxing Wang, Yuhong Huo and Junhai Luo study the synchronization of a class of uncertain fractional-order neural networks subject to external disturbances and disturbed system parameters [4]. In Approximate Analytical Solutions of Time Fractional Whitham–Broer–Kaup Equations by a Residual Power Series Method, Linjun Wang and Xumei Chen apply a new analytic iterative technique, called the residual power series method, to time fractional Whitham–Broer–Kaup equations [5]. In Characterization of Complex Fractionated Atrial Electrograms by Sample Entropy: An International Multi-Center Study, Eva Cirugeda-Roldán, Daniel Novak, Vaclav Kremen, David Cuesta-Frau, Matthias Keller, Armin Luik and Martina Srutova propose the use of sample entropy for discerning between non-fractionated and fractionated atrial electrograms, and for characterizing the degree of trial electrograms regularity [6]. The paper Chaos on the Vallis Model for El Niño with Fractional Operators, by Badr Saad T. Alkahtani and Abdon Atangana, investigates the Vallis model for El Niño. The authors study and compare both integer and non-integer order versions of the model [7].