# Latest Developments on Synchronization in Dynamical Systems and Neural Networks

Synchronization describes the linking of two chaotic systems with a common signal or signals, the trajectories of one of the systems will converge to the same values as the other and they will remain in step with each other. When this occurs, the synchronization is said to be structurally stable. The idea of ...

Synchronization describes the linking of two chaotic systems with a common signal or signals, the trajectories of one of the systems will converge to the same values as the other and they will remain in step with each other. When this occurs, the synchronization is said to be structurally stable. The idea of synchronization has been applied to several well-known nonlinear dynamical systems, chaotic systems, neural networks models, secure communications and more by researchers, scientists, and engineers from all parts of the world. Nowadays the concept of synchronization in dynamic systems is used in different areas of nature such as physical science, medical science, engineering, etc., by the scientific community where it is showing potential for developing innovative technologies.

Chaotic systems are often referred to as dynamic systems, describing the interactions of types in sufficient non-linearity. The study of non-linear dynamics has gained immense popularity over the last few decades. This is due in part to the utilization of neural networking models (neural networks). Neural networks, in dynamical systems, are based on simplified mathematical descriptions of the physical structure and mechanism of a chaotic system, allowing it to be synchronized with another system. This Research Topic seeks to call to the research community to bring together papers that explore which types of synchronization and how their advances in neural networking can be applied to nonlinear dynamic systems. The mathematical model of a dynamical system is expressed either as a differential equation over a continuous or discrete time. The governing differential equation or the difference equation expresses the present states of the system inferred by using the previous states of the system as a set of constant inputs and fixed parameters. This results in a nonlinear dynamical system that can evaluate a complex computation problem for large-scale systems; which is made possible by the growing power of modern computers and improved computational techniques. This is particularly the case when neural network models seek out to learn the complexities of dynamical systems, which is done in part via the process of synchronization.

This Research Topic offers researchers the opportunity to showcase their work, discuss advances in the field and exchange their idea on ways to further refine and develop the application of neural networks to dynamical systems.

The principal objective of this issue is to gather papers working within the latest advances on synchronization in dynamical systems and neural networks.

The area of interest is wide and includes several categories as follows:
• Synchronization
• Nonlinear Dynamical Systems
• Stability Analysis
• Secure Communication
• Dynamics of Chaotic systems
• Fractional Order Dynamical Systems
• Difference Equation
• Control Systems
• Neural Networks
• Artificial Neural Networks

Keywords: Nonlinear Dynamical Systems, Stability Analysis, Synchronization, Dynamics of Chaotic systems, Fractional Order Dynamical Systems, Difference equation, Control Systems, Neural Networks, Artificial neural networks

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