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Non-autonomous dynamical systems generate cocycles w.r.t. a flow. We give conditions for the existence of attractors for cocycles based on the so-called pull back convergence. These conditions will be applied to the non-autonomous Navier Stokes equation. In particular. we do not need compactness assumption for the time dependent coefficients of this equation.

In this chapter, basic life-intelligence, and the evolution and co-evolution dynamics of eco-systems are further examined and compared to certain processes in human organizations. A special reference on human thinking systems as intelligence/consciousness sources, information decoders, information processors and complex adaptive systems (CAS) is re-emphasized. In addition, the significance of connectivity, communications, engagement, and orgmindfulness is analyzed with respect to the Abilene paradox, defensive routines and dialogue, as well as the human agent-agent/system micro-structure and micro-dynamic. The individual local self-centric (local self-enrichment processes) and the global orgcentric (global forces) evolutionary dynamics of intelligent human organizations (no global optimality) and their interacting agents (no optimal rationality) are investigated more explicitly with the exploitation of the certain complexity properties. It is observed that local order (stability of agents and networks/subsystem) is highly critical in human dynamic. It is beneficial to recognize that the intelligent complex adaptive dynamic (iCAD) driving an intelligent human organization (iCAS) is not similar to complex adaptive dynamic (CAD) in totality. This recognition provides a significant foundation and better understanding of the intelligent human organizational micro-structure and dynamic.

Essentially, there is a vital need for the transformed mindset, thinking, values, and expectations of human agents (leaders, actors, and non-actors) to be better synchronized. The intelligent person model (an ideal set of attributes) is introduced to substantiate the criticality of new vital characteristics of the human interacting agents in intelligent human organizations. Primarily, intelligent persons (a new category of agents, in particular, intelligence leaders and synergists) are concurrently intelligence/consciousness-centric, complexity-centric and network-centric. The new set of attributes includes high self-powered, intrinsic leadership, information decoding, smarter evolver, emergent strategist, and futurist capabilities. For instance, such a person is in a better position to function as a smarter evolver and emergent strategist that helps to bind a group (network, community, corporation, nation) of human thinking systems more optimally by elevating the quality of collective intelligence in the organization through better mindfulness, orgmindfulness, symbiosis, self-transcending constructions, co-evolution; deeper recognition of the characteristics of the rugged landscape and red queen race; innovative exploitation of relativistic complexity, and possessing futuristic thinking. Apparently, the presence of intelligent persons/agents will lead to a redefinition in leadership and governance strategy.

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.

In this chapter, the intelligence-associated evolution and co-evolution dynamics of eco-systems are examined and compared to the processes of human organizations as stipulated in some existing organization theories. A special focus on businesses as complex adaptive systems is also included. The individual local self-centric and the global org-centric evolutionary dynamics of intelligent organizations and their interacting agents are more explicitly investigated. Subsequently, the intelligent person model is introduced to substantiate the needs to transform. How the intelligent person function as a smarter evolver helps to bind a group of human thinking systems and elevate the collective intelligence of the organization through mindfulness, orgmindfulness and co-evolution is also analyzed. (For better understanding, some concepts that are introduced earlier are further reinforced and better integrated in this chapter.)

We built basics of the qualitative theory of the continuous-time difference equations x(t + 1) = f(x(t)), t ∈ ℝ⁺, with the method of going to the infinite-dimensional dynamical system induced by the equation. For a study of this system we suggest an approach to analyzing the asymptotic dynamics of general nondissipative systems on continuous functions spaces. The use of this approach allows us to derive properties of the solutions from that of the ω-limit sets of trajectories of the corresponding dynamical system. In particular, typical continuous solutions are shown to tend (in Hausdorff metric for graphs) to upper semicontinuous functions whose graphs are, in wide conditions, fractal; there may exist especially nonregular solutions described asymptotically exactly by random processes. We introduce the notion of self-stochasticity in deterministic systems — a situation when the global attractor contains random functions. Substantiated is a scenario for a spatial-temporal chaos in distributed parameters systems with regular dynamics on attractor: The attractor consists of cycles only and the onset of chaos results from the very complicated structure of attractor “points” which are elements of some function space (different from the space of smooth functions). We develop a method to research into boundary value problems for partial differential equations, that bases on their reduction to difference equations.