International Symposium The Economic Crisis: Time For A Paradigm Shift ~ . Towards a Systems Approach

January 24-25, 2013 Universitat de València - Facultat d'Economia

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New Paradigm of Innovation Management

based on Synergetic and Multifractal

Approaches

Rashid Zaynetdinov

Professor of Innovative Technology, ScD, PhD

Moscow State University of Railway Engineering (MIIT), Russia.

e-mail: zri7755@gmail.com

ABSTRACT

The new paradigm of innovation management is based on the exploration, analysis and modeling

the features and states (such as non-equilibrium, instable, nonstationary) of innovative

technological and socio-economic system as well as concomitant transient processes taking into

account their development in time. Among the features of the system and concomitant innovation

and investment processes which were explored, it is possible to notice such features as openness,

irreversibility, nondifferentiability, long term feedbacks, discontinuity, complexity, ability to self-

organization, self-similarity, nonlinear nature, etc.

Until a profound understanding the features and states of the complex system and transient

processes is achieved, and until they can be reliably modeled, there is clearly no hope of

effectively controlling it, except of course through empiricism.

For increasing the efficiency of innovation management in technologies and society we

investigate the innovation processes from point of view of synergetics. We consider the

innovation in the complex socio-economic system as open, non-equilibrium, dissipative, active

system, capable for self-organization. For analysis of evolution, associated with the

technological innovations, we present a synergetic model that links the dynamics of

informational entropy with the self-organization process in the system. We analyze the local

element's behavior in different “modes of being” (the old, transient and new). Formulas for

dynamics of the entropy flow and its rate are obtained with respect to innovation process and

investment flow in the system.

It is shown that an open innovative system responds to a strong change of being conditions by

steep growth of the entropy flow up to a maximum value at the critical point. The self-

organization process is destruction of the dissipative structures at the previous hierarchical

level, exhausting its possibilities, and emergence of new more complicated and more advanced

dissipative structures, corresponding to the changed being conditions. A system comes back to a

steady state due to inflow of the information from the outside or redistribution of the

informational entropy between the hierarchical levels of the system.

Obtained mathematical expressions make it possible to predict the moment when the critical

point (that is stochastic analogue of bifurcation point) will be reached. That is the moment of

crisis, in other words the moment of maximum uncertainty and instability in the complex system

when small fluctuations become amplified up to a macroscopic scale. In such a system the new

International Symposium

The Economic Crisis: Time For A Paradigm Shift ~ . Towards a Systems Approach

January 24-25, 2013 - Universitat de València

2

attractors of technological and socio-economic development can emerge spontaneously. Some

typical trajectories of transition to attractors of technological development were selected. The

bifurcation point may drive the system into a completely new state and thus become the driving

force of the system’s development. The transition to a new level of development goes from the

disorder to the order, through the phenomenon of instability in points of bifurcation.

The bifurcation moment’s functional dependence ¬of the distribution function for stochastic¬

process of external influences on system is revealed. By means of changing the parameters of

input flows from external sources into the system (for example, investment and information

flows),¬¬¬ we have possibility to effect the moment when the bifurcation point will be reached.

We can try to influence on system before and at the bifurcation point. We cannot predict, which

trajectory the innovative system will go after the bifurcation point. But we can try to create

optimum conditions for successful passage through the bifurcation point in a desirable

direction,¬ and also to take appropriate measures to direct¬¬ innovative system on a favorable

way of development.

Self-organization process in complex system results in self-affine sequence of meaningful events,

associated with innovations. We do not know whether some temporal pattern is hidden in an

apparently disordered set of the innovation events. The multifractal theory is a good basis for

revealing such an order and for describing a flow of the multiscale events in the course of time.

The multifractal approach provides a deeper understanding the nature of the innovative event

flow and evidence for the existence of a multiplicative process hidden in a temporal pattern of

the innovation event sequence. In order to verify the fractality of data sets a wavelet analysis was

carried out. We used the continuous wavelet transform for revealing the intrinsic temporal

structure of the datasets about innovation processes.

Deeper insight into process of innovations, their prediction and management is to be gained by

using the synergetical and multifractal approaches to the self-organization processes in the

complex innovative socio-economic systems.