scholarly journals Period-doubling cascades and mode interactions in coupled systems

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2030005-2030006
Author(s):  
P. J. Aston ◽  
H. Mir
Keyword(s):  
Period Doubling ◽  
Coupled Systems ◽  
Mode Interactions

MULTI-PARAMETER CRITICALITY IN CHUA'S CIRCUIT AT PERIOD-DOUBLING TRANSITION TO CHAOS

1996 ◽  
Vol 06 (01) ◽  
pp. 119-148 ◽  
Author(s):  
A. P. KUZNETSOV ◽  
S. P. KUZNETSOV ◽  
I. R. SATAEV ◽  
L. O. CHUA
Keyword(s):  
Period Doubling ◽  
Coupled Systems ◽  
Strict Sense ◽  
Chua’S Circuit ◽  
Dynamical Equations ◽  
Scaling Properties ◽  
Unidirectional Coupling ◽  
Chua's Circuit ◽  
Transition To Chaos ◽  
Two Systems

Investigation of non-Feigenbaum types of period-doubling universality is undertaken for a single Chua's circuit and for two systems with a unidirectional coupling. Some codimension-2 critical situations are found numerically that were known earlier for bimodal 1D maps. However, the simplest of them (tricritical) does not survive in a strict sense when the exact dynamical equations are used instead of the 1D map approximation. In coupled systems double Feigenbaum's point and bicritical behavior are found and studied. Scaling properties that are the same as in two logistic maps with a unidirectional coupling are illustrated.

scholarly journals Complex Dynamics and Synchronization in a System of Magnetically Coupled Colpitts Oscillators

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
L. K. Kana ◽  
A. Fomethe ◽  
H. B. Fotsin ◽  
E. T. Wembe ◽  
A. I. Moukengue
Keyword(s):  
Complex Dynamics ◽  
Spectral Characteristics ◽  
Period Doubling ◽  
Magnetic Coupling ◽  
Coupled System ◽  
Coupling Factor ◽  
Coupled Systems ◽  
Numerical Exploration ◽  
The Stability ◽  
Parameter Ranges

We propose the use of a simple, cheap, and easy technique for the study of dynamic and synchronization of the coupled systems: effects of the magnetic coupling on the dynamics and of synchronization of two Colpitts oscillators (wireless interaction). We derive a smooth mathematical model to describe the dynamic system. The stability of the equilibrium states is investigated. The coupled system exhibits spectral characteristics such as chaos and hyperchaos in some parameter ranges of the coupling. The numerical exploration of the dynamics system reveals various bifurcations scenarios including period-doubling and interior crisis transitions to chaos. Moreover, various interesting dynamical phenomena such as transient chaos, coexistence of solution, and multistability (hysteresis) are observed when the magnetic coupling factor varies. Theoretical reasons for such phenomena are provided and experimentally confirmed with practical measurements in a wireless transfer.

Period-doubling mode interactions with circular symmetry

1990 ◽  
Vol 44 (3) ◽  
pp. 340-396 ◽  
Author(s):  
John David Crawford ◽  
Edgar Knobloch ◽  
Hermann Riecke
Keyword(s):  
Period Doubling ◽  
Circular Symmetry ◽  
Mode Interactions

Terrorist teams as loosely coupled systems.

2018 ◽  
Vol 73 (4) ◽  
pp. 491-503 ◽  
Author(s):  
Matthias Spitzmuller ◽  
Guihyun Park
Keyword(s):  
Coupled Systems ◽  
Loosely Coupled Systems ◽  
Loosely Coupled

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

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