Chaotic Modelling and Simulation: Analysis of Chaotic Models, Attractors and Forms

@inproceedings{Skiadas2008ChaoticMA,
  title={Chaotic Modelling and Simulation: Analysis of Chaotic Models, Attractors and Forms},
  author={C. Skiadas},
  year={2008}
}
Introduction Chaos in Differential Equations Systems Chaos in Difference Equation Systems More Complex Structures Chaos and the Universe Odds and Ends and Milestones Models and Modeling Introduction Model Construction Modeling Techniques Chaotic Analysis and Simulation Deterministic, Stochastic, and Chaotic Models The Logistic Model The Logistic Map The Bifurcation Diagram Other Models with Similar Behavior Models with Different Chaotic Behavior The GRM1 Chaotic Model Further Discussion The… Expand

Figures from this paper

Local Stable or Unstable Regions in 2-Dimensional Chaotic Forms: Examples and Simulations
We analyze 2-dimensional chaotic forms resulting from very simple systems based on two chaotic characteristics that is rotation and parallel movement or translation in geometric terms. Re ection isExpand
Threshold Method for Control of Chaotic Oscillations
TLDR
This classical Chua’s circuit that generates a chaotic and controlled attractor with a fixed period can be used in modern systems transmitting and receiving information. Expand
Transient Processes in a Model Multilayer Nanosystem with Nonlinear Fractal Oscillator
Within the framework of the two-point model the states of deformation and stress fields of a fractal quantum dot, the stochastic state of discrete lattice in a model multilayer nanosystem areExpand
THRESHOLD METHOD FOR CONTROL OF CHAOTIC OSCILLATIONS
FORMULATION OF THE PROBLEM. Chaos is the most interdisciplinary thematic areas; it includes very interesting, complex, nonlinear phenomena that have been intensively studied and regard many differentExpand
Simulating annealing and neural networks for chaotic time series forecasting
This paper examines how neural networks that use simulating annealing for training is relative to linear and polynomial approximations to forecast a time series that is generated by the chaoticExpand
Rotations-Expansion-Reflections Chaotic Modelling with Singularities in Higher Dimensions
Rotation – Expansion – Translation – Reflection chaotic models show despite of its simple generators complex structures that resemble in 2 dimensions without referring to any material property wellExpand
Simplified numerical methods used for the approximations of chaotic solutions of dynamical systems
TLDR
This work presents simplified numerical methods for chaotic attractors that are implemented for Rössler and Lorenz systems using a rescaling technique that uses integrating factors. Expand
Multilevel thresholding based on Chaotic Darwinian Particle Swarm Optimization for segmentation of satellite images
TLDR
An improved variant of Darwinian PSO algorithm based on chaotic functions that replaces random sequences by chaotic sequences mitigating the problem of premature convergence and provides better convergence characteristics and segmentation results as compared with existing algorithms. Expand
Guaranteed state and parameter estimation for one-dimensional chaotic system
  • A. S. Sheludko, V. Shiryaev
  • Mathematics
  • 2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)
  • 2016
In this article, the problem of state and parameter estimation is considered for an one-dimensional chaotic system. Based on the guaranteed approach and interval computations, the proposed algorithmExpand
Computer modeling and practical realization of chaotic circuit with a light-emitting diode
A novel simple autonomous optoelectronic circuit that demonstrate chaotic behavior is presented. In this circuit a lightemitting diode is a simple optoelectronic element. The mathematical model thatExpand
...
1
2
3
4
...

References

SHOWING 1-10 OF 695 REFERENCES
High-dimensional chaotic behavior in systems with time-delayed feedback
Abstract The nature of high-dimensional chaos exhibited by a class of delay-differential equation is investigated by various methods. This delay-differential equation models systems with time delayedExpand
Bifurcations in a system described by a nonlinear differential equation with delay.
TLDR
All the bifurcation phenomena observed, including the blue sky disappearance (boundary crisis) of a chaotic attractor, show geometric structures which are consistent with familiar low-dimensional center-manifold descriptions. Expand
Homoclinic chaos in chemical systems
Abstract We first focus on complex dynamical phenomena generated by chemical kinetics in homogeneous media. We comment on the alternating sequences of periodic and chaotic states observed in someExpand
Chaos in numerical analysis of ordinary differential equations
Abstract The discretisation of the ordinary nonlinear differential equation d y d t = y(1−y) by the entral difference scheme is studied for fixed mesh size. In the usual numerical computation, thisExpand
An Introduction To Chaotic Dynamical Systems
Part One: One-Dimensional Dynamics Examples of Dynamical Systems Preliminaries from Calculus Elementary Definitions Hyperbolicity An example: the quadratic family An Example: the Quadratic FamilyExpand
Chaos in deterministic systems: Strange attractors, turbulence, and applications in chemical engineering
Abstract It is now well established that seemingly innocuous dynamical systems, dissipative or not, can produce complicated phase trajectories and, eventually, chaos. There is now an enormous amountExpand
Different Types of Chaos in Two Simple Differential Equations
Abstract Different types of chaotic flow are possible in the 3-dimensional state spaces of two simple non-linear differential equations. The first equation consists of a 2-variable, double-focusExpand
Exploring and Simulating Chaotic Advection:A Difference Equations Approach
This paper explores the chaotic properties of an advection system expressed in difference equations form. In the beginning the Aref's blinking vortex system is examined. Then several new lines areExpand
Simultaneous modeling of nonlinear deterministic and stochastic dynamics
Abstract We present a method which can simultaneously model the nonlinear deterministic and stochastic dynamics underlying an observed time series. It is formulated to treat Markov processes inExpand
The Chaotic Hierarchy
Abstract The complexity of dynamical behavior possible in nonlinear (for example, electronic) systems depends only on the number of state variables involved. Single-variable dissipative dynamicalExpand
...
1
2
3
4
5
...