Narrow Results

Turing instability is a prominent feature of reaction–diffusion systems, which is widely investigated in many fields, such as ecology, neurobiology, chemistry. However, although the inhomogeneous diffusion between prey and predators exist in their network space, there are few considerations on how network diffusion affects the stability of prey–predator models. Therefore, in this paper we study the pattern dynamics of a modified reaction–diffusion Holling–Tanner prey–predator model over a random network. Specifically, we study the relationship between the node degrees of the random network and the eigenvalues of the network Laplacian matrix. Then, we obtain conditions under which the network system instability, Hopf bifurcation as well as Turing bifurcation occur. Also, we find an approximate Turing instability region of the diffusion coefficient and the connection probability of the network. Finally, we apply the mean-field approximation theory with numerical simulation to confirm the correctness of our results. The instability region indicates the random migration of the prey and predators among different communities.

Due to the finite speed of signal transmission, time delay is a common phenomenon in neuronal systems. The spatiotemporal dynamics of the FitzHugh–Rinzel model with time delay and diffusion in a random network are investigated in this paper. The conditions for Turing instability and Hopf bifurcation are obtained by linear stability analysis. It is found that the stability of the system changes with the time delay. Then the critical time delay for the state transition of the system is derived. Moreover, it is shown that Turing pattern is related to the network diffusion and connection probability. The increase of the diffusion coefficient will change the spatiotemporal pattern of the system. In addition, the system will achieve firing synchronization as the connection probability increases. Finally, numerical simulation verifies the theoretical results.

Recent theoretical studies on network robustness have focused primarily on attacks by random selection and global vision, but numerous real-life networks suffer from proximity-based breakdown. Here we introduce the multi-hop generalized core percolation on complex networks, where nodes with degree less than $k$ and their neighbors within $L$-hop distance are removed progressively from the network. The resulting subgraph is referred to as $G(k,L)$-core, extending the recently proposed $Gk$-core and classical core of a network. We develop analytical frameworks based upon generating function formalism and rate equation method, showing for instance continuous phase transition for $G(2,1)$-core and discontinuous phase transition for $G(k,L)$-core with any other combination of $k$ and $L$. We test our theoretical results on synthetic homogeneous and heterogeneous networks, as well as on a selection of large-scale real-world networks. This unravels, e.g., a unique crossover phenomenon rooted in heterogeneous networks, which raises a caution that endeavor to promote network-level robustness could backfire when multi-hop tracing is involved.

Gaussian graphical model (GGM)-based method, a key approach to reverse engineering biological networks, uses partial correlation to measure conditional dependence between two variables by controlling the contribution from other variables. After estimating partial correlation coefficients, one of the most critical processes in network construction is to control the false discovery rate (FDR) to assess the significant associations among variables. Various FDR methods have been proposed mainly for biomarker discovery, but it still remains unclear which FDR method performs better for network construction. Furthermore, there is no study to see the effect of the network structure on network construction. We selected the six FDR methods, the linear step-up procedure (BH95), the adaptive linear step-up procedure (BH00), Efron's local FDR (LFDR), Benjamini–Yekutieli's step-up procedure (BY01), Storey's q-value procedure (Storey01), and Storey–Taylor–Siegmund's adaptive step-up procedure (STS04), to evaluate their performances on network construction. We further considered two network structures, random and scale-free networks, to investigate their influence on network construction. Both simulated data and real experimental data suggest that STS04 provides the highest true positive rate (TPR) or F1 score, while BY01 has the highest positive predictive value (PPV) in network construction. In addition, no significant effect of the network structure is found on FDR methods.

The spread of infectious diseases often presents the emergent properties, which leads to more difficulties in prevention and treatment. In this paper, the SIR model with both delay and network is investigated to show the emergent properties of the infectious diseases’ spread. The stability of the SIR model with a delay and two delay is analyzed to illustrate the effect of delay on the periodic outbreak of the epidemic. Then the stability conditions of Hopf bifurcation are derived by using central manifold to obtain the direction of bifurcation, which is vital for the generation of emergent behavior. Also, numerical simulation shows that the connection probability can affect the types of the spatio-temporal patterns, further induces the emergent properties. Finally, the emergent properties of COVID-19 are explained by the above results.

The first section of this chapter is an introduction to relativistic complexity (a significant component of the intelligent organization theory). The presence of intense intelligence/consciousness-centricity and 3^rd order stability-centricity in the human world renders complexity relativistic. The impact of the human mental space is so tremendous that complexity is in the mind of the beholder, and predictability becomes highly subjective. In this situation, the state of relativistic static equilibrium may be beneficial. Certain spaces of complexity appear as spaces of relativistic order with surface patterns becoming more apparent. Such spaces must be creatively explored and exploited (higher exploratory capacity) leading to a more advanced level of intelligence advantage. In this respect, effective self-transcending constructions, high self-organizing capacity and emergence-intelligence capacity are significant attributes that the new leadership and governance system in intelligent human organizations must exploit. Holistically, the two strategies focus on concurrent exploitation of intelligence/consciousness-centricity and relative complexity, and optimizing the more comprehensive contributions of the integrated deliberate and emergent strategy.

Many issues/problems that present human organizations (nations, political systems, communities, business organizations, markets) are encountering due to accelerating changes (mindset, thinking, values, perceptions, expectations, redefined boundaries and high interactive dynamics) that cannot be well-managed with traditional knowledge and hierarchical practices are affecting governance and governance systems. Fundamentally, governance deals with power, interest, and conflict. The traditional governance systems are hierarchical, highly directed, controlled and managed, and the relational aspect has not been allocated sufficient priority resulting in extensive disparities. In the current complex dynamical and high interdependency environment, its weaknesses and constraints are highly apparent. The latter includes ‘space-time compression’; incoherency in thinking, values, perceptions, and expectations between the leadership and the other agents; diversification in stakeholders’ needs not accommodated; and constraints of current governance theories. Thus, a new theory that provides a more ‘realistic’ foundation is essential for deeper contemplation.

Primarily, recognizing the inherent strengths of human agents and the fundamental constraints/weaknesses of human organizations is a key foundation towards better adaptation, leadership, governance, resilience and sustainability. In all human organizations, the agents are intrinsic intense intelligence/consciousness sources that could easily transform their behavioral schemata. This observation contradicts the Newtonian/design paradigm, as the organizational dynamic of human agents is complex, nonlinear, constantly/continuously changing with limited predictability. In addition, human agents are self-centric, self-powered, stability-centric, independent and interdependent, network-centric and self-organizing due to high awareness. In this situation, high self-organizing capacity and emergence-intelligence capacity are new niches. However, this phenomenon can create new opportunities, innovation, and elevates competiveness; or destruction.

In particular, effective leadership and governance are spontaneously emerging key requirements in all human groupings — a primary trait for human collective survival. Historically, many organizations disintegrated because of the weaknesses in leadership and governance. Currently, with more knowledge-intensive and higher participative new agents (self-powered intrinsic leadership) possessing modified attributes that are dissimilar from the older generations (also due to the deeper integration of the economic, social, political, and environmental perspective), reduces consensus and collaboration, and renders governance and leadership even more nonlinear or dysfunctional. In particular, the traditional governance systems of more organizations are manifesting their constraints and incompetency, including incoherency due to new values and cultural pressure, and the wider spread of self-organizing networks. The emergent of informal networks is a more commonly observed phenomenon worldwide. Apparently, a deeper comprehension on the diminishing effect of the traditional organizational thinking (political, social, economic), governance capacity, precise strategic planning, decision making, hierarchical structure, communications and engagement, empowerment leadership, management, operations, and the highly nonlinear relational parameter is essential. Apparently, new principles of governance must emerge (intelligent human organization > thinking system + feeling system).

The new paradigmatic path of the intelligence governance strategy that exploits intelligence/consciousness-centricity, complexity-centricity, and network-centricity concurrently, introduces a new basic strategic path towards better adaptive governance and acceptance governance. The latter focuses on integrating self-powered self-organizing governance, reducing direct governance, and increasing e-governance and network-centric governance as a new necessity. In this case, the merits of adopting the intelligence leadership strategic approach simultaneously are more apparent. Hence, the new governance focal points must include more and better interconnected actors, the critical ability of self-organizing communications (supported by mobile/social media development), immersion of leadership nodes in networks (better exploitation of e-governance), increasing coherency of complex networks (exploiting interdependency of network of networks, and better network management), and elevating self-transcending constructions capability (higher self-organizing governance capacity and emergence-intelligence capacity) that better facilitates emergence through multi-level and ‘multi-lateral’ dynamics (complex adaptive networks <=> intelligent networks). Thus, the intelligence governance strategy emphasizes that mass lateral collectivity (acceptance governance) rather than selective enforced hierarchical empowerment as the more constructive approach in the present contact. In particular, the stabilityinducing role of leaders and institutions are critical. Apparently, optimizing the ‘everybody is in charge’ phenomenon (whenever necessary) is a more viable option.