CONSTANT-PHASE-INDUCED CONTROL OF CHAOTIC CHARGED PARTICLES IN THE FIELD OF A WAVE PACKET

2013 ◽  
Vol 23 (06) ◽  
pp. 1330022
Author(s):  
RICARDO CHACÓN
Keyword(s):  
Charged Particle ◽  
Wave Packet ◽  
Finite Number ◽  
Lyapunov Exponents ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Charged Particles ◽  
Melnikov Method ◽  
Wide Range ◽  
Range Of Values

It is shown that the dissipative chaotic dynamics of a charged particle in the field of a wave packet with an arbitrary but finite number of harmonics can be reliably suppressed by judiciously varying the constant phase of the main harmonic, ϕ0, while keeping null the corresponding constant phases of the remaining harmonics. The dependence of the chaotic threshold on the wave packet parameters is predicted theoretically (Melnikov method) and confirmed numerically (Lyapunov exponents). In particular, it is shown that ϕ0 is effective at suppressing the chaotic behavior existing when ϕ0 = 0 over a wide range of values of the wave packet width, while the remaining parameters are kept constant.

scholarly journals A computational framework for finding parameter sets associated with chaotic dynamics

2021 ◽  
pp. 1-11
Author(s):  
S. Koshy-Chenthittayil ◽  
E. Dimitrova ◽  
E.W. Jenkins ◽  
B.C. Dean
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Parameter Space ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Computational Framework ◽  
Independent Variables ◽  
Systems Model ◽  
Small Support

Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we use existing software tools (COPASI, R) to explore dynamical systems and uncover regions with positive Lyapunov exponents where thus chaos exists. We evaluate the ability of the software’s optimization algorithms to find these positive values with several dynamical systems used to model biological populations. The algorithms have been able to identify parameter sets which lead to positive Lyapunov exponents, even when those exponents lie in regions with small support. For one of the examined systems, we observed that positive Lyapunov exponents were not uncovered when executing a search over the parameter space with small spacings between values of the independent variables.

scholarly journals A novel family of 1-D robust chaotic maps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dhrubajyoti Mandal
Keyword(s):  
Mathematical Models ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Infinite Family ◽  
Practical Applications ◽  
Smooth Maps ◽  
Wide Range ◽  
Chaotic Signals ◽  
Piecewise Smooth Maps ◽  
Parameter Values

AbstractChaotic dynamics of various continuous and discrete-time mathematical models are used frequently in many practical applications. Many of these applications demand the chaotic behavior of the model to be robust. Therefore, it has been always a challenge to find mathematical models which exhibit robust chaotic dynamics. In the existing literature there exist a very few studies of robust chaos generators based on simple 1-D mathematical models. In this paper, we have proposed an infinite family consisting of simple one-dimensional piecewise smooth maps which can be effectively used to generate robust chaotic signals over a wide range of the parameter values.

scholarly journals Dynamics of the Modified n-Degree Lorenz System

2019 ◽  
Vol 4 (2) ◽  
pp. 315-330 ◽  
Author(s):  
Sk. Sarif Hassan ◽  
Moole Parameswar Reddy ◽  
Ranjeet Kumar Rout
Keyword(s):  
Dynamical Systems ◽  
Fixed Points ◽  
Lyapunov Exponents ◽  
Limit Cycle ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Lorenz Model ◽  
Periodic Behavior ◽  
Chaotic Model

AbstractThe Lorenz model is one of the most studied dynamical systems. Chaotic dynamics of several modified models of the classical Lorenz system are studied. In this article, a new chaotic model is introduced and studied computationally. By finding the fixed points, the eigenvalues of the Jacobian, and the Lyapunov exponents. Transition from convergence behavior to the periodic behavior (limit cycle) are observed by varying the degree of the system. Also transiting from periodic behavior to the chaotic behavior are seen by changing the degree of the system.

CHAOS IN A NEAR-INTEGRABLE HAMILTONIAN LATTICE

2002 ◽  
Vol 12 (08) ◽  
pp. 1743-1754 ◽  
Author(s):  
VASSILIOS M. ROTHOS ◽  
CHRIS ANTONOPOULOS ◽  
LAMBROS DROSSOS
Keyword(s):  
Lyapunov Exponents ◽  
Numerical Experiments ◽  
Chaotic Dynamics ◽  
Large Scale ◽  
Hamiltonian Structure ◽  
Chaotic Behavior ◽  
Original System ◽  
Homoclinic Orbits ◽  
Hamiltonian Lattice ◽  
Whiskered Tori

We study the chaotic dynamics of a near-integrable Hamiltonian Ablowitz–Ladik lattice, which is N + 2-dimensional if N is even (N + 1, if N is odd) and possesses, for all N, a circle of unstable equilibria at ε = 0, whose homoclinic orbits are shown to persist for ε ≠ 0 on whiskered tori. The persistence of homoclinic orbits is established through Mel'nikov conditions, directly from the Hamiltonian structure of the equations. Numerical experiments which combine space portraits and Lyapunov exponents are performed for the perturbed Ablowitz–Ladik lattice and large scale chaotic behavior is observed in the vicinity of the circle of unstable equilibria in the ε = 0 case. We conjecture that this large scale chaos is due to the occurrence of saddle-center type fixed points in a perturbed 1 d.o.f Hamiltonian to which the original system can be reduced for all N. As ε > 0 increases, the transient character of this chaotic behavior becomes apparent as the positive Lyapunov exponents steadily increase and the orbits escape to infinity.

Global Bifurcations of Mean Electric Field in Plasma L–H Transition Under External Bounded Noise Excitation

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
C. Nono Dueyou Buckjohn ◽  
M. Siewe Siewe ◽  
C. Tchawoua ◽  
T. C. Kofane
Keyword(s):  
Electric Field ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Power Spectra ◽  
Melnikov Method ◽  
Radial Electric Field ◽  
Model Parameters ◽  
Global Bifurcations ◽  
Bounded Noise ◽  
Noise Perturbation

In this paper, global bifurcations and chaotic dynamics under bounded noise perturbation for the nonlinear normalized radial electric field near plasma are investigated using the Melnikov method. From this analysis, we get criteria that could be useful for designing the model parameters so that the appearance of chaos could be induced (when heating particles) or run out for quiescent H-mode appearance. For this purpose, we use a test of chaos to verify our prediction. We find that, chaos could be enhanced by noise amplitude growing. The results of numerical simulations also reveal that noise intensity modifies the attractor size through power spectra, correlation function, and Poincaré map. The criterion from the Melnikov method which is used to analytically predict the existence of chaotic behavior of the normalized radial electric field in plasma could be a valid tool for predicting harmful parameters values involved in experiment on Tokamak L–H transition.

scholarly journals Collective Oscillations in Many Electron Atoms. II. Scattering and Slowing Down

1974 ◽  
Vol 27 (2) ◽  
pp. 169
Author(s):  
JJ Monaghan
Keyword(s):  
Charged Particle ◽  
Charged Particles ◽  
Fermi Model ◽  
Thomas Fermi ◽  
Slowing Down ◽  
Wide Range ◽  
Collective Oscillations

The slowing down of fast charged particles by their interaction with many electron atoms is considered using the hydrodynamic version of the Thomas-Fermi model. The agreement obtained with experiment is excellent over a wide range of parameters but worsens as the velocity of the charged particle decreases.

Melnikov method approach to control of homoclinic/heteroclinic chaos by weak harmonic excitations

2006 ◽  
Vol 364 (1846) ◽  
pp. 2335-2351 ◽  
Author(s):  
Ricardo Chacón
Keyword(s):  
Wave Packet ◽  
Charged Particles ◽  
Melnikov Method ◽  
Potential Well ◽  
Electrostatic Wave ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Harmonic Excitations ◽  
Low Dimensional ◽  
Method Approach

A review on the application of Melnikov's method to control homoclinic and heteroclinic chaos in low-dimensional, non-autonomous and dissipative oscillator systems by weak harmonic excitations is presented, including diverse applications, such as chaotic escape from a potential well, chaotic solitons in Frenkel–Kontorova chains and chaotic-charged particles in the field of an electrostatic wave packet.

scholarly journals Chaotic dynamics of fractional Vallis system for El-Niño

2019 ◽  
Vol 22 (3) ◽  
pp. 825-842
Author(s):  
Amey Deshpande ◽  
Varsha Daftardar-Gejji
Keyword(s):  
El Niño ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
El Nino ◽  
Critical Value ◽  
Additional Parameter ◽  
Weather Phenomenon ◽  
The Lorenz System ◽  
Range Of Values

Abstract Vallis proposed a simple model for El-Niño weather phenomenon (referred as Vallis system) by adding an additional parameter p to the Lorenz system. He showed that the chaotic behavior of the Vallis system is related to the El-Niño effect. In the present article we study fractional version of Vallis system in detail. We investigate bifurcations and chaos present in the fractional Vallis system and the effect of variation of system parameter p. It is observed that the range of values of parameter p for which the Vallis system is chaotic, reduces with the reduction of the fractional order. Further we analyze the incommensurate fractional Vallis system and find the critical value below which the system loses chaos. We also synchronize Vallis system with Bhalekar-Gejji system.

CHAOS IN A THREE-DIMENSIONAL CANCER MODEL

2010 ◽  
Vol 20 (01) ◽  
pp. 71-79 ◽  
Author(s):  
MEHMET ITIK ◽  
STEPHEN P. BANKS
Keyword(s):  
Immune System ◽  
Lyapunov Exponents ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Dynamical Model ◽  
Parameter Range ◽  
Cancer Growth ◽  
Cancer Model ◽  
Lyapunov Dimension

In this study, we develop a new dynamical model of cancer growth, which includes the interactions between tumour cells, healthy tissue cells, and activated immune system cells, clearly leading to chaotic behavior. We explain the biological relevance of our model and the ways in which it differs from the existing ones. We perform equilibria analysis, indicate the conditions where chaotic dynamics can be observed, and show rigorously the existence of chaos by calculating the Lyapunov exponents and the Lyapunov dimension of the system. Moreover, we demonstrate that Shilnikov's theorem is valid in the parameter range of interest.

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