Structure of Phase Portraits of Nonlinear Dynamical Systems

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

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Generating Fully Bounded Chaotic Attractors

International Journal of Artificial Life Research ◽

10.4018/jalr.2011070104 ◽

2011 ◽

Vol 2 (3) ◽

pp. 36-42

Author(s):

Zeraoulia Elhadj

Keyword(s):

Dynamical Systems ◽

Nonlinear Dynamical Systems ◽

Dynamical Behavior ◽

Phase Portraits ◽

Chaotic Attractors ◽

Nonlinear Dynamical ◽

Dynamical Properties ◽

The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

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COVID-19 outbreaks follow narrow paths: A computational phase portrait approach based on nonlinear physics and synergetics

International Journal of Modern Physics C ◽

10.1142/s0129183121501102 ◽

2021 ◽

pp. 2150110

Author(s):

T. D. Frank

Keyword(s):

Dynamical Systems ◽

Nonlinear Dynamical Systems ◽

Order Parameters ◽

Phase Portraits ◽

Mathematical Epidemiology ◽

Epidemiological Models ◽

Amplitude Equations ◽

State Spaces ◽

Nonlinear Dynamical ◽

Intervention Measures

From the perspective of mathematical epidemiology, COVID-19 epidemics emerge due to instabilities in epidemiological systems. It is shown that the COVID-19 outbreaks follow highly specified paths in epidemiological state spaces. These paths are described by phase portraits that can be readily computed from epidemiological models defined in terms of nonlinear dynamical systems. The paths are predicted by order parameters and amplitude equations that are well known in nonlinear physics and synergetics to exist at instability points. The approach is illustrated for SIR, SEIR and SEIAR models and epidemic outbreaks in China, Italy and West Africa. Identifying such COVID-19 order parameters may help in forecasting COVID-19 epidemics and predicting the impacts of intervention measures.

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