Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance

Small, Michael

doi:10.1142/5722

Cited by 186 publications

(227 citation statements)

References 0 publications

Supporting

Mentioning

215

Contrasting

Unclassified

Order By: Relevance

“…The corresponding time series consist of periodic parts of oscillation without a common structure. 3 Nevertheless, closely starting trajectories remain close to each other during time evolution. The third class contains dynamical systems with chaotic attractors which are non-periodic, with an exponential dependence on initial conditions for bounded orbits.…”

Section: From Linear To Nonlinear and Stochastic Dynamicsmentioning

confidence: 88%

Challenges of Complexity in the 21st Century. An Interdisciplinary Introduction

Mainzer¹

2009

European Review

View full text Add to dashboard Cite

The theory of nonlinear complex systems has become a proven problem-solving approach in the natural sciences from cosmic and quantum systems to cellular organisms and the brain. Even in modern engineering science self-organizing systems are developed to manage complex networks and processes. It is now recognized that many of our ecological, social, economic, and political problems are also of a global, complex, and nonlinear nature. Modern evolutionary economics can be modelled in the framework of complex systems and nonlinear dynamics. Historically, evolutionary economics was inspired by Schumpeterian concepts of business cycles and innovation dynamics. What are the laws of sociodynamics? What can we learn from nonlinear dynamics for complexity management in social, economic, financial and political systems? Is self-organization an acceptable strategy to handle the complexity in firms, institutions and organizations? The world-wide crisis of financial markets and economies is a challenge for complexity research. Misleading concepts of linear thinking and mild randomness (e.g. Gaussian distributions of Brownian motion) must be overcome by new approaches of nonlinear mathematics (e.g. non-Gaussian distribution), modelling the wild randomness of turbulence at the stock markets. Systemic crises need systemic answers. Nevertheless, human cognitive capabilities are often overwhelmed by the complexity of nonlinear systems they are forced to manage. Traditional mathematical decision theory assumed perfect rationality of economic agents (homo oeconomicus). Herbert Simon, Nobel Prize laureate of economics and one of the leading pioneers of systems science and cognitive science, introduced the principle of bounded rationality. Therefore, we need new insights into the factual microeconomic behaviour of economic agents by methods of humanities, cognitive and social sciences, which are sometimes called ‘experimental economics’. Social and economic dynamics are interdisciplinary challenges of modern complexity research.

show abstract

Section: From Linear To Nonlinear and Stochastic Dynamicsmentioning

confidence: 88%

Challenges of Complexity in the 21st Century. An Interdisciplinary Introduction

Mainzer¹

2009

European Review

View full text Add to dashboard Cite

show abstract

“…In the case of multivariate time series, a further scope may be the causal relations (also called coupling or information directions) between pairs of components. See [27] for a general introduction to nonlinear time-series analysis with applications.…”

Section: (G) Time-series Analysismentioning

confidence: 99%

Mathematical methods in medicine: neuroscience, cardiology and pathology

Amigó

Small

2017

Phil. Trans. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.

show abstract

“…As a result one of the challenges that scientists try to master is to extend the set of linear models with nonlinear ones. There are many propositions of nonlinear models to be found along with identification procedures dedicated for them (see [34], [38], and [36]). …”

Section: Introductionmentioning

confidence: 99%

Identification of stable elementary bilinear time-series model

Maliński

2016

Archives of Control Sciences

View full text Add to dashboard Cite

The paper presents new approach to estimation of the coefficients of an elementary bilinear time series model (EB). Until now, a lot of authors have considered different identifiability conditions for EB models which implicated different identifiability ranges for the model coefficient. However, all of these ranges have a common feature namely they are significantly narrower than the stability range of the EB model. This paper proposes a simple but efficient solution which makes an estimation of the EB model coefficient possible within its entire stability range.

show abstract

Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance

Cited by 186 publications

References 0 publications

Challenges of Complexity in the 21st Century. An Interdisciplinary Introduction

Challenges of Complexity in the 21st Century. An Interdisciplinary Introduction

Mathematical methods in medicine: neuroscience, cardiology and pathology

Identification of stable elementary bilinear time-series model

Contact Info

Product

Resources

About