Hybrid Intelligent Systems for Non-linear Dynamical Systems

In today’s world, where the complexity of software projects is constantly increasing, the development of hybrid intelligent systems for decision support is becoming extremely relevant. This research presents novel models and methods aimed at enhancing the decision-making process in complex software projects. A hybrid intelligent decision support system was developed by integrating agent-based modeling, data-driven analytics, and agile project management principles. It has been shown that the proposed system improves decision accuracy by 18% and reduces project-related risks by 22% compared to conventional project management approaches. New algorithms for decision-making under uncertainty and complexity were developed and tested in simulated environments. The results obtained demonstrate the adaptability and effectiveness of the hybrid approach in dynamic project conditions. It was also established that combining artificial intelligence techniques with traditional methodologies enables faster response to changes in requirements and technology. Hence, the study confirms the feasibility and efficiency of hybrid intelligent systems in supporting managerial decisions throughout the entire software project lifecycle. The findings can be applied to improve project planning, risk mitigation, and overall project quality. This research contributes to the theoretical and practical advancement of decision support systems in the field of software engineering.

This paper is dedicated to the research of the dynamics of development and interactions among several scientific communities in the field of fuzzy logic and soft computing. This analysis was performed with the help of the following characteristics: conferences participants’ renewal, the level of cooperation in scientific communities, participation of one community’s key players in activities of the other ones, comparative number of most active participants in each community, uniformity of key players’ participation in different conferences.

This paper presents how to apply a newly developed general theory for the global transversality and tangency of flows in n-dimensional nonlinear dynamical systems to a 2-D nonlinear dynamical system (i.e. a periodically forced, damped Duffing oscillator). The global tangency and transversality of the periodic and chaotic motions to the separatrix for such a nonlinear system are discussed to help us understand the complexity of chaos in nonlinear dynamical systems. This paper presents the concept that the global transversality and tangency to the separatrix are independent of the Melnikov function (or the energy increment). Chaos in nonlinear dynamical systems makes the exact energy increment quantity to be chaotic no matter if the nonlinear dynamical systems have separatrices or not. The simple zero of the Melnikov function cannot be used to simply determine the existence of chaos in nonlinear dynamical systems. Through this paper, the expectation is that, from now on, one can use the alternative aspect to look into the complexity of chaos in nonlinear dynamical systems. Therefore, in this paper, the analytical conditions for global transversality and tangency of 2-D nonlinear dynamical systems are presented. The first integral quantity increment (i.e. the energy increment) for a certain time interval is achieved for periodic flows and chaos in the 2-D nonlinear dynamical systems. Under the perturbation assumptions and convergent conditions, the Melnikov function is recovered from the first integral quantity increment. A periodically forced, damped Duffing oscillator with a separatrix is investigated as a sampled problem. The corresponding analytical conditions for the global transversality and tangency to the separatrix are obtained and verified by numerical simulations. The switching planes and the corresponding local and global mappings are defined on the separatrix. The mapping structures are developed for local and global periodic flows passing through the separatrix. The mapping structures of global chaos in the damped Duffing oscillator are also discussed. Bifurcation scenarios of the damped Duffing oscillator are presented through the traditional Poincaré mapping section and the switching planes. The first integral quantity increment (i.e. L-function) is presented to observe the periodicity of flows. In addition, the global tangency of periodic flows in such an oscillator is measured by the G-function and G(1)-function, and is verified by numerical simulations. The first integral quantity increment of periodic flows is zero for their complete periodic cycles. Numerical simulations of chaos in such a Duffing oscillator are carried out through the Poincaré mapping sections. The conservative energy distribution, G-function and L-function along the displacement of Poincaré mapping points are presented to observe the complexity of chaos. The first integral quantity increment (i.e. L-function) of chaotic flows at the Poincaré mapping points is nonzero and chaotic. The switching planes of chaos are presented on the separatrix for a better understanding of the global transversality to the separatrix. The switching point distribution on the separatrix is presented and the switching G-function on the separatrix is given to show the global transversality of chaos on the separatrix. The analytical conditions are obtained from the new theory rather than the Melnikov method. The new conditions for the global transversality and tangency are more accurate and independent of the small parameters.

BackgroundExpert knowledge in journal articles is an important source of data for reconstructing biological pathways and creating new hypotheses. An important need for medical research is to integrate this data with high throughput sources to build useful models that span several scales. Researchers traditionally use mental models of pathways to integrate information and development new hypotheses. Unfortunately, the amount of information is often overwhelming and these are inadequate for predicting the dynamic response of complex pathways. Hierarchical computational models that allow exploration of semi-quantitative dynamics are useful systems biology tools for theoreticians, experimentalists and clinicians and may provide a means for cross-communication.ResultsA novel approach for biological pathway modeling based on hybrid intelligent systems or soft computing technologies is presented here. Intelligent hybrid systems, which refers to several related computing methods such as fuzzy logic, neural nets, genetic algorithms, and statistical analysis, has become ubiquitous in engineering applications for complex control system modeling and design. Biological pathways may be considered to be complex control systems, which medicine tries to manipulate to achieve desired results. Thus, hybrid intelligent systems may provide a useful tool for modeling biological system dynamics and computational exploration of new drug targets. A new modeling approach based on these methods is presented in the context of hedgehog regulation of the cell cycle in granule cells. Code and input files can be found at the Bionet website: www.chip.ord/~wbosl/Software/Bionet.ConclusionThis paper presents the algorithmic methods needed for modeling complicated biochemical dynamics using rule-based models to represent expert knowledge in the context of cell cycle regulation and tumor growth. A notable feature of this modeling approach is that it allows biologists to build complex models from their knowledge base without the need to translate that knowledge into mathematical form. Dynamics on several levels, from molecular pathways to tissue growth, are seamlessly integrated. A number of common network motifs are examined and used to build a model of hedgehog regulation of the cell cycle in cerebellar neurons, which is believed to play a key role in the etiology of medulloblastoma, a devastating childhood brain cancer.

In this chapter, we offer a nonlinear dynamical systems perspective on the development of chronic pain (see also Young and Chapman, 2006). We incorporate the simpler understanding of systems, as “the whole being greater than the sum of the parts,” into contemporary systems theory. We consider systems theory both in terms of its original expression as chaos theory and more advanced versions related to complexity theory. By framing chronic pain within the perspective of nonlinear dynamical systems theory, a transdisciplinary model, some phenomena that are difficult to explain in terms of other models become more transparent, revealing the multifactorial nature of pain. We grant that nonlinear dynamical systems theory is not easy to understand in its details, although systems theory in general has an intuitive appeal. Therefore, theorists, assessors, and practitioners alike need to study and integrate this approach into their work with chronic pain patients. Moreover, the model is consistent with the theme of this book, and with forensic psychology, in general, because it provides a multicausal understanding of chronic pain. Williams and Arrigo (2002) have applied chaos and complexity theory to forensic psychology, examining areas such as dangerousness and its prediction, civil commitment, and the right to refuse mental health treatment. However, the work does not address specific conditions such as chronic pain.

Modeling of Microblogging Social Networks: Dynamical System vs. Random Dynamical System

A method for identifying nonlinear dynamic systems with noise is proposed by using probabilistic universal learning networks (PrULNs). PrULNs are extensions of universal learning networks (ULNs). ULNs form a superset of neural networks and were proposed to provide a universal framework for modeling and control of nonlinear large-scale complex systems. But the ULN does not provide any stochastic characteristics of the signals propagating through it. The PrULNs are equipped with machinery to calculate stochastic properties of signals and to train network parameters so that the signals behave with the pre-specified stochastic properties. On the other hand it is generally recognized that there exists an overfitting problem when identification of nonlinear dynamic systems with noise is done by neural networks. In this paper, it is shown from simulation results of identification of a nonlinear robot dynamics that PrULNs are useful for avoiding the overfitting.

The development of technology demands Computer Science graduates to have interdisciplinary knowledge and skills. Traditional curricula are less adaptive in addressing the dynamic industry needs and focus on developing soft skills. This article discusses the design of an interdisciplinary curriculum based on KKNI for Computer Science programs with a focus on soft computing and intelligent systems. This curriculum design integrates knowledge and skills from various disciplines, with an emphasis on the development of soft skills. The curriculum structure is divided into two tracks: the Mandatory Track focusing on the fundamental foundations of Computer Science and soft skills, and the Elective Track focusing on deepening interests and talents in the field of soft computing and intelligent systems, such as Artificial Neural Networks, Microcontrollers, Data Mining, Embedded Systems, Fuzzy Logic, and Computer Vision. This research adopts a Research and Development (R&D) approach with the ADDIE model. Data are collected through surveys, interviews, and document analysis. It is expected that this curriculum design will produce Computer Science graduates with comprehensive, adaptive knowledge and skills, ready for the digital era workforce, particularly in the field of soft computing and intelligent systems.

Years ago, many researchers proposed that chaos theory could provide a kind of universal theory of the qualitative behavior of all dynamical systems. Thus it could provide a solid mathematical foundation for unifying efforts to address the three really fundamental questions of basic science: (1) what is life?; (2) what is mind or intelligence?; (3) what are the underlying physical laws of the universe? Chaos theory is essentially a recent extension of a larger field of mathematics which it is part of: nonlinear system dynamics (NSD). It mainly addresses systems governed by Ordinary Differential Equations (ODE) or their discrete-time cousins. Because the vast bulk of models now used in computational neuroscience are ODE models, it is only natural that neuroscience has developed great interest in the use of NSD as a tool for analyzing and designing neural network models. Walter Freeman, in particular, has played a seminal role in describing how chaos theory can be used in computational neuroscience, in his classical models of the olfactory system, described in articles in Scientific American and many scientific journals and IJCNN proceedings. His colleague Morris Hirsch in mathematics has helped provide a solid foundation for this work. This work has helped to inspire many efforts throughout the world to use chaos as a design principle in computer systems and in artificial neural network (ANN) design. Recently, however, several issues or questions have begun to emerge, some at Berkeley and some in other places. The author discusses these questions and their implications.

Elements of mathematical phenomenology of self-organization nonlinear dynamical systems: Synergetics and fractional calculus approach

Chaos theory can be used for quantitative dynamics of uncertainty and finding order in its perturbances. Chaos theory is largely a colloquial notion and is referred to as an analysis of non-linear dynamical systems. The studies devoted to linear dynamical systems and theories of complexity involve studies of turbulence, or, more precisely, the transfer from stability to turbulence. The dynamical system by its nature does not follow long-term forecasts. There are two reasons for the unpredictability. Dynamical systems involve both feedback and critical levels. To paraphrase, one can say that a dynamical system forms a system of non-linear feedback. The most important properties of the system include: sensitivity to the change of the initial conditions, occurrence of critical points and a fractal dimension. Non-linear dynamical systems tend to have more than one solution. The case often is that the number of solutions is huge or even infinite. A visual representation of the data forms a finite space called the phase space of the system. The number of dimensions in the space is determined by the number of variable presents in the system. If there are two or three variables, it is possible to visually examine the data. In case of a larger number of dimensions, the data are examined with the use of mathematical data. Another term used in non-linear dynamical systems is the attractor. This is an area of a equilibrium of non-linear system within a time series. A system which aims to achieve an equilibrium in the form of a single value has a point attractor. Besides, there are phase attractors, which form periodic cycles or orbits in space forming a limit cycle. An attractor, in which none of the points in the space overlaps and whose orbits do not cross but both originate in the same area of phase space, is called strange attractor. Such attractors in contrast to point attractors are non-periodic and predominantly have a fractal dimension [10,11].

This chapter introduces the basic concepts of dynamical systems theory and several basic mathematical methods for controlling chaos. The main goal of this chapter is to provide an introduction to and a summary of the theory of dynamical systems, with particular emphasis on fractal theory, chaos theory, and chaos control. We first define what is meant by a dynamical system, then we define an attractor, and then the concept of the fractal dimension of a geometrical object. We also define the Lyapunov exponents as a measure of the chaotic behavior of a dynamical system. On the other hand, the fractal dimension can be used to classify geometrical objects because it measures the complexity of an object. The chapter also describes mathematical methods for controlling chaos in dynamic systems. These methods can be used to control a real dynamic system; however, due to efficiency and accuracy requirements we were forced to use fuzzy logic to model the uncertainty, which is present when numerical simulations are performed. We also describe in this chapter a new theory of chaos using fuzzy logic techniques. Chaotic behavior in nonlinear dynamical systems is very difficult to detect and control. Part of the problem is that mathematical results for chaos are difficult to use in many cases, and even if one could use them there is an underlying uncertainty in the accuracy of the numerical simulations of the dynamical systems. For this reason, we can model the uncertainty of detecting the range of values where chaos occurs, using fuzzy set theory. Using fuzzy sets, we can build a theory of fuzzy chaos, where we can use fuzzy sets to describe the behaviors of a system. We illustrate our approach with two cases: Chua’s circuit and Duffing’s oscillator.

The article discusses the application of the theory of dynamic chaos to the study of social phenomena. Appeal to the origins of the creation of the theory of dynamic chaos in natural science (A. Poincaré, I. Prigogine, E. Lorenz, and others) revealed nonlinear dynamic systems in the natural environment (turbulent flows, atmosphere, biological populations, etc.). The category of “chaos” is now firmly established in the arsenal of the social sciences and humanities, although only recently it referred exclusively to natural science knowledge (the theory of chaos in mathematics, physics, biology, etc.). In synergetics, for the first time, the description of self-organization processes as a mutual transition of order and chaos was proposed by I.R. Prigogine.But in the social sciences such systems are society, its economic, political and other spheres, which have the properties of non-closure, instability and non-linear development. In Ukrainian philosophical thought, one of the first works in which the problem of the development of nonlinear self-developing systems was highlighted was the work of I.S. Dobronravova (1991). Scientific monograph I.V. Yershova-Babenko (1992) also had a significant impact on the development of studies of complex non-linear systems, since for the first time the system of the human psyche was considered as a non-linear self-organized system. The psycho-synergetic model of social reality is based on the fact that social reality is a psychomeric environment, i.e. a complex nonlinear system consisting of other complex nonlinear integrity, which are determined by phase transitions between different states of chaos and order. The application of chaos theory is also possible at the micro and macro levels of social research, which is presented by Ukrainian researchers in synergetics (I. S. Dobronravova, L. Finkel) and in psychosynergetics (I.V. Yershova-Babenko), L. Bevzenko and others.

Modeling and control of nonlinear systems using an Adaptive LAMDA approach

This study characterized drought propagation in the Han River basin based on chaos theory and nonlinear dynamic systems. The nonlinear complexity of drought propagation, specifically between meteorological and hydrological droughts, was identified using convergent cross-mapping and phase-space reconstruction techniques. The analysis results on the causality of drought propagation between meteorological and hydrological droughts revealed that among the 24 middle-sized watersheds of the Han River basin, 11 watersheds had bidirectional causality, and the other 13 watersheds had one-directional causality. This study also confirmed that there were large correlations between the two drought types when 12 of the 13 watersheds with one-directional causality had a lag time of 4 months and the remaining watershed had a delay time of 7 months. The complexity of the interaction between different droughts was confirmed through adjustments of key parameters, such as the embedding dimension, time delay, correlation dimension, and Lyapunov exponent. The approach proposed in this study made it possible to analyze the nonlinear dynamic characteristics of drought propagation, which have not been analyzed in previous studies.