Synergy among the various components of national agricultural innovation systems (AISs) promotes agricultural development. This paper investigated the innovation synergy among the various innovation elements of national AISs. First, we developed a synergy analysis model consisting of three innovation variables (innovation allocation, innovation output, and innovation potentiality) and one control variable (government policy supports). Secondly, a broad set of innovation indicators was selected to describe the innovation variables and the control variable, and the solutions of the order parameter equation were then calculated to investigate the self-organized synergistic patterns of a panel of the Group of Twenty (G20) countries. The empirical results indicated the following. (1) All of the G20 countries' national AISs had the potential to evolve into more advanced self-organized synergistic states under current government policy support. Furthermore, all of the developing countries were in the active period of synergy, showing stronger synergistic rising powers. However, most of the developed countries were in the stable or general period of synergy, in which synergistic rising powers were relatively weaker; (2) Stronger government policy supports played a positive role in promoting the interaction and collaboration among innovation elements and promoted the national AIS to evolve into a more advanced self-organized synergistic state. This study has important implications for understanding the complex innovation synergy of national AISs, as well as for the design and implementation of agricultural innovation strategies for policy-makers.Sustainability 2018, 10, 3385 2 of 20 in agricultural production through collaborative interaction with each other, so as to reach the coordination of economic, social, and ecological benefits in one country [6].As agricultural innovation becomes increasingly viewed as a far more complex and less linear process, it has become more and more difficult to identify the complex relations that constitute innovation processes. Recently, the agricultural innovation system (AIS) approach [5,7] has become increasingly popular as a tool for analyzing agricultural innovation processes [8][9][10]. The AIS approach evolved from a transition from the simplistic linear or pipeline model to a complex non-linear or network model of agricultural innovation [11,12]. The AIS approach provides a conceptual framework for the integrated analysis of (1) complex agricultural problems [13]; (2) innovation capacity in the agricultural system to solve these problems [14]; and (3) the structure and function of the AIS, which can enhance or constrain innovation capacities in the agricultural system [8,9,11]. Applying the AIS [5,7] framework is particularly promising for sustainable agricultural development, because it can help identify where the most binding constraints on agricultural innovation are located and how better to target interventions to remove such constraints [15].Innovation performance depends no...