The digital revolution characterized by the current ICT and digital technology enables us to map what happens in this physical space into its cyber counterpart as if we have two simultaneously co-existing societies. One is a society of human agents and `things’ in the physical space; the other is the `incarnation’ of the former in the cyber space, further empowered by a myriad of software agents. The relation between the two societies provides a challenge for the science of complexity, since the mapping between the two is not just unidirectional (self-imaging), but also bidirectional (cyclical looping). The cyber space can not only passively reflect the shape of the physical space, but more often than not it can actively shape that shape, which in turn results in the two societies having a feedback relationship with each other as they constantly co-evolve. Understanding their coevolutionary dynamics becomes a research agenda that one cannot afford to have missing when looking ahead into the future well-being of humans. In the past, we have seen many individual subjects being developed as walks in between the two societies, but works which address the complex interactions between the two are still limited.

The complexity interactions of the two societies are currently manifested in one of the following three forms: transformation, extension, and repercussion. First, transformation. The emergence of the cyber space as an image of the physical space prompts us to search for new solution principles for tackling problems that are otherwise difficult to solve in the physical world. Mathematically and technically speaking, one can first transform the problem into the cyber space, use tools or software agents available in the cyber space to solve the problem, and transfer the solution back to the physical space. We have seen many such kind of applications, usually emblazoned with a logo of smartness. Second, extension. Once the cyber society is founded, it is better treated as an autonomous entity, having its own life, and having its own problems to solve. In this regard, can the mechanisms that we learned from the physical space, such as the market, community, management, or governance be applicable to tackling problems appearing in the cyber space? The introduction of new auction mechanisms in the cyber space, called internet auctions, is one of the earlier examples. Finally, there are repercussion. The previous two interactive relations address cooperation between the physical society and the cyber society. However, the cyber space can also bring threats to the physical space. The impact of the cyber space is not limited to jobs and business opportunities, but can come on a much larger scale as a cyber-tsunami to overwhelmingly alter the operations of the labor market, the financial markets, and the democratic system, and even permeate the human decision-making routines.

The aim of this Special Issue is to bring together original research and review articles discussing the complexity of the co-evolution between physical space and cyber space. Submissions should provide context of co-evolutionary and emergent dynamics.

Potential topics include but are not limited to the following:

• Complexity theory of cyber-physical interactions
• Cyber-physical Interactions in financial market
• Blockchain, cryptocurrencies and decentralized finance
• Cyber-physical interactions in labor markets
• Cyber-physical interactions in management
• Cyber-physical interactions in governance
• Cyber-physical interactions in human decision making
• Smartness and cyber-physical interactions
• History of cyber-physical interactions