A New Megastable Oscillator with Rational and Irrational Parameters

2019 ◽  
Vol 29 (13) ◽  
pp. 1950176 ◽  
Author(s):  
Zhen Wang ◽  
Ibrahim Ismael Hamarash ◽  
Payam Sadeghi Shabestari ◽  
Sajad Jafari
Keyword(s):  
Dynamical System ◽  
Infinite Number ◽  
Limit Cycles ◽  
Nonlinear Oscillator ◽  
Analog Circuit ◽  
Strange Attractors ◽  
Two Dimensional ◽  
System A ◽  
New System

In this paper, a new two-dimensional nonlinear oscillator with an unusual sequence of rational and irrational parameters is introduced. This oscillator has endless coexisting limit cycles, which make it a megastable dynamical system. By periodically forcing this system, a new system is designed which is capable of exhibiting an infinite number of coexisting asymmetric torus and strange attractors. This system is implemented by an analog circuit, and its Hamiltonian energy is calculated.

scholarly journals A Giga-Stable Oscillator with Hidden and Self-Excited Attractors: A Megastable Oscillator Forced by His Twin

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 535 ◽  
Author(s):  
Thoai Phu Vo ◽  
Yeganeh Shaverdi ◽  
Abdul Jalil M. Khalaf ◽  
Fawaz E. Alsaadi ◽  
Tasawar Hayat ◽  
...  
Keyword(s):  
Nonlinear System ◽  
Limit Cycle ◽  
Infinite Number ◽  
Nonlinear Oscillator ◽  
Original System ◽  
Strange Attractors ◽  
Two Dimensional ◽  
Coexisting Attractors ◽  
Basin Of Attractions

In this paper, inspired by a newly proposed two-dimensional nonlinear oscillator with an infinite number of coexisting attractors, a modified nonlinear oscillator is proposed. The original system has an exciting feature of having layer–layer coexisting attractors. One of these attractors is self-excited while the rest are hidden. By forcing this system with its twin, a new four-dimensional nonlinear system is obtained which has an infinite number of coexisting torus attractors, strange attractors, and limit cycle attractors. The entropy, energy, and homogeneity of attractors’ images and their basin of attractions are calculated and reported, which showed an increase in the complexity of attractors when changing the bifurcation parameters.

PERIODIC INHIBITION OF LIVING PACEMAKER NEURONS (I): LOCKED, INTERMITTENT, MESSY, AND HOPPING BEHAVIORS

1991 ◽  
Vol 01 (03) ◽  
pp. 549-581 ◽  
Author(s):  
J. P. SEGUNDO ◽  
E. ALTSHULER ◽  
M. STIBER ◽  
A. GARFINKEL
Keyword(s):  
Nonlinear Dynamics ◽  
Point Process ◽  
Limit Cycles ◽  
Nonlinear Oscillator ◽  
Strange Attractors ◽  
Synaptic Inhibition ◽  
Pacemaker Neurons ◽  
Pacemaker Neuron ◽  
Exhaustive List

This communication is concerned with an embodiment of periodic nonlinear oscillator driving, the synaptic inhibition of one spike-producing pacemaker neuron by another. Data came from a prototypical living synapse. Analyses centered on a prolonged condition between the transients following the onset and cessation of inhibition. Evaluations were guided by point process mathematics and nonlinear dynamics. A rich and exhaustive list of discharge forms, described precisely and canonically, was observed across different inhibitory rates. Previously unrecognized at synapses, most forms were identified with several well known types from nonlinear dynamics. Ordered by decreasing regularities, they were locked, intermittent (including walk-throughs), messy (including erratic and stammerings) and hopping. Each is discussed within physiological and formal contexts. It is conjectured that (i) locked, intermittent and messy forms reflect limit cycles on 2-tori, quasiperiodic orbits and strange attractors, (ii) noise in neurons hovering around threshold contributes to certain intermittent and stammering behaviors, and (iii) hopping either reflects an attractor with several portions or is nonstationary and noise-induced.

A Modified Multistable Chaotic Oscillator

2018 ◽  
Vol 28 (07) ◽  
pp. 1850085 ◽  
Author(s):  
Zhouchao Wei ◽  
Viet-Thanh Pham ◽  
Abdul Jalil M. Khalaf ◽  
Jacques Kengne ◽  
Sajad Jafari
Keyword(s):  
Chaotic System ◽  
Limit Cycles ◽  
Initial Conditions ◽  
Chaotic Oscillator ◽  
Two Dimensional ◽  
Different Types ◽  
New System

In this paper, by modifying a known two-dimensional oscillator, we obtain an interesting new oscillator with coexisting limit cycles and point attractors. Then by changing this new system to its forced version and choosing a proper set of parameters, we introduce a chaotic system with some very interesting features. In this system, not only can we see the coexistence of different types of attractors, but also a fascinating phenomenon: some initial conditions can escape from the gravity of nearby attractors and travel far away before being trapped in an attractor beyond the usual access.

A Novel No-Equilibrium Chaotic System with Multiwing Butterfly Attractors

2015 ◽  
Vol 25 (04) ◽  
pp. 1550056 ◽  
Author(s):  
Fadhil Rahma Tahir ◽  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Xiong Wang
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
State Feedback ◽  
Equilibrium Points ◽  
Research Topic ◽  
Feedback Controller ◽  
Strange Attractors ◽  
State Feedback Controller ◽  
New Chaotic System ◽  
New System

Discovering unknown features of no-equilibrium systems with hidden strange attractors is an attractive research topic. This paper presents a novel no-equilibrium chaotic system that is constructed by using a state feedback controller. Interestingly, the new system can exhibit multiwing butterfly attractors. Moreover, a new chaotic system with an infinite number of equilibrium points, which can generate multiscroll attractors, is also proposed by applying the introduced methodology.

New Methods for Analyzing Water Pollutants

1982 ◽  
Vol 14 (4-5) ◽  
pp. 59-71 ◽  
Author(s):  
L H Keith ◽  
R C Hall ◽  
R C Hanisch ◽  
R G Landolt ◽  
J E Henderson
Keyword(s):  
Amino Acids ◽  
Gas Chromatography ◽  
Two Dimensional ◽  
Gas Chromatograph ◽  
New Class ◽  
New Methods ◽  
System A ◽  
Drinking Waters ◽  
Computer Controlled ◽  
Nitrogen Containing Compounds

Two new methods have been developed to analyze for organic pollutants in water. The first, two-dimensional gas chromatography, using post detector peak recycling (PDPR), involves the use of a computer-controlled gas Chromatograph to selectively trap compounds of interest and rechromatograph them on a second column, recycling them through the same detector again. The second employs a new detector system, a thermally modulated electron capture detector (TMECD). Both methods were used to demonstrate their utility by applying them to the analysis of a new class of potentially ubiquitous anthropoaqueous pollutants in drinking waters- -haloacetonitriles. These newly identified compounds are produced from certain amino acids and other nitrogen-containing compounds reacting with chlorine during the disinfection stage of treatment.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

A DYNAMICAL SYSTEM WITH CHAOTIC BEHAVIOR

1989 ◽  
Vol 03 (15) ◽  
pp. 1185-1188 ◽  
Author(s):  
J. SEIMENIS
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Infinite Number ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Hamiltonian Dynamical Systems

We develop a method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. We apply this method to the system [Formula: see text] We study the case a → 0 and we find that in this case the system has an infinite number of period dubling bifurcations.

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