A Complete Investigation of the Effect of External Force on a 3D Megastable Oscillator

2020 ◽  
Vol 30 (01) ◽  
pp. 2050012 ◽  
Author(s):  
Yongjian Liu ◽  
Abdul Jalil M. Khalaf ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Bifurcation Diagram ◽  
Limit Cycle ◽  
Strange Attractor ◽  
Dynamical Behavior ◽  
System A ◽  
Extreme Multistability ◽  
Forced Oscillator ◽  
Multistable Systems ◽  
Complete Investigation

Multistability is an essential topic in nonlinear dynamics. Recently, two critical subsets of multistable systems have been introduced: systems with extreme multistability and systems with megastability. In this paper, based on a newly introduced megastable system, a megastable forced oscillator is introduced. The effect of adding a forcing term and its parameters on the dynamical behavior of the designed system is investigated. By the help of bifurcation diagram and Lyapunov exponents, it is shown that the modified oscillator can show a variety of dynamical solutions including limit cycle, torus, and strange attractor.

Simplest Megastable Chaotic Oscillator

2019 ◽  
Vol 29 (13) ◽  
pp. 1950187 ◽  
Author(s):  
Sajad Jafari ◽  
Karthikeyan Rajagopal ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Viet-Thanh Pham
Keyword(s):  
Nonlinear Dynamics ◽  
Bifurcation Diagram ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Chaotic Oscillator ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Dynamical Properties ◽  
New System

Recently, chaotic systems with hidden attractors and multistability have been of great interest in the field of chaos and nonlinear dynamics. Two special categories of systems with multistability are systems with extreme multistability and systems with megastability. In this paper, the simplest (yet) megastable chaotic oscillator is designed and introduced. Dynamical properties of this new system are completely investigated through tools like bifurcation diagram, Lyapunov exponents, and basin of attraction. It is shown that between its countable infinite coexisting attractors, only one is self-excited and the rest are hidden.

Numerical Analysis of a Novel 3D Chaotic System with Period-Subtracting Structures

2021 ◽  
Vol 31 (11) ◽  
pp. 2150169
Author(s):  
Maryam Zolfaghari-Nejad ◽  
Hossein Hassanpoor ◽  
Mostafa Charmi
Keyword(s):  
Numerical Analysis ◽  
Periodic Solutions ◽  
Limit Cycle ◽  
Chaotic System ◽  
Strange Attractor ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Period Doubling ◽  
Dynamical Evolution ◽  
Point Attractor

In this work, we present a novel three-dimensional chaotic system with only two cubic nonlinear terms. Dynamical behavior of the system reveals a period-subtracting bifurcation structure containing all [Formula: see text]th-order ([Formula: see text]) periods that are found in the dynamical evolution of the novel system concerning different values of parameters. The new system could be evolved into different states such as point attractor, limit cycle, strange attractor and butterfly strange attractor by changing the parameters. Also, the system is multistable, which implies another feature of a chaotic system known as the coexistence of numerous spiral attractors with one limit cycle under different initial values. Furthermore, bifurcation analysis reveals interesting phenomena such as period-doubling route to chaos, antimonotonicity, periodic solutions, and quasi-periodic motion. In the meantime, the existence of periodic solutions is confirmed via constructed Poincaré return maps. In addition, by studying the influence of system parameters on complexity, it is confirmed that the chaotic system has high spectral entropy. Numerical analysis indicates that the system has a wide variety of strong dynamics. Finally, a message coding application of the proposed system is developed based on periodic solutions, which indicates the importance of studying periodic solutions in dynamical systems.

Dynamics of a Supported Cylinder in Axial Flow

2011 ◽  
Vol 99-100 ◽  
pp. 1059-1062
Author(s):  
Ji Duo Jin ◽  
Ning Li ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Analysis ◽  
Numerical Simulations ◽  
Nonlinear Model ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Viscous Force ◽  
Friction Drag ◽  
Flutter Instability ◽  
Nonlinear Force

The nonlinear dynamics are studied for a supported cylinder subjected to axial flow. A nonlinear model is presented for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are the quadratic viscous force and the structural nonlinear force induced by the lateral motions of the cylinder. Using two-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain the flutter instability found in the experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. The effect of the friction drag coefficients on the behavior of the system is investigated.

Nonlinear Dynamics and Application of the Four Dimensional Autonomous Hyper-Chaotic System

2014 ◽  
Author(s):  
Ge Kai ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Differential Equations ◽  
Chaotic System ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Phase Portraits ◽  
State Variables ◽  
Chaotic Motions ◽  
Finance System

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.

An explicit plethora of soliton solutions for a new microtubules transmission lines model: A fractional comparison

2021 ◽  
Author(s):  
Nauman Raza ◽  
Ziyad A. Alhussain
Keyword(s):  
Nonlinear Dynamics ◽  
Transmission Lines ◽  
Fractional Derivatives ◽  
Intracellular Transport ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Governing System ◽  
Parameter Values ◽  
Fractional Parameter

This paper introduces a new fractional electrical microtubules transmission lines model in the sense of Atangana–Baleanu and beta derivatives to comprehend nonlinear dynamics of the governing system. This structure possesses one of the most important parts in cellular process biology and fractional parameter incorporates the memory effects in microtubules. Also, microtubules are extremely beneficial in cell motility, signaling and intracellular transport. The new extended direct algebraic method is a compelling and persuasive integrating scheme to extract soliton solutions. The retrieved solutions include dark, bright and singular solitons. This model executes a prominent part in exhibiting the wave transmission in nonlinear systems. The novelty and advantage of the proposed method are portrayed by applying it to this model and its dynamical behavior is depicted by 3D and 2D plots. A comparative study of two fractional derivatives at distinct fractional parameter values and graphics of sensitivity analysis is also carried out in this paper.

scholarly journals Dynamical Behaviour in Two Prey-Predator System with Persistence

2016 ◽  
Vol 16 ◽  
pp. 20-37
Author(s):  
V. Madhusudanan ◽  
S. Vijaya
Keyword(s):  
Limit Cycle ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Dynamical Behaviour ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Interior Equilibrium ◽  
Trivial Equilibrium ◽  
Necessary And Sufficient

In this work, the dynamical behavior of the system with two preys and one predator population is investigated. The predator exhibits a Holling type II response to one prey which is harvested and a Beddington-DeAngelis functional response to the other prey. The boundedness of the system is analyzed. We examine the occurrence of positive equilibrium points and stability of the system at those points. At trivial equilibrium E0and axial equilibrium (E1); the system is found to be unstable. Also we obtain the necessary and sufficient conditions for existence of interior equilibrium point (E6) and local and global stability of the system at the interior equilibrium (E6): Depending upon the existence of limit cycle, the persistence condition is established for the system. The numerical simulation infer that varying the parameters such as e and λ1it is possible to change the dynamical behavior of the system from limit cycle to stable spiral. It is also observed that the harvesting rate plays a crucial role in stabilizing the system.

scholarly journals Big Bang Bifurcations in the Tantalus Oscillator Under Biphasic Perturbations

2019 ◽  
Vol 29 (02) ◽  
pp. 1950023
Author(s):  
Humberto Arce ◽  
Araceli Torres ◽  
Augusto Cabrera ◽  
Martín Alarcón ◽  
Carlos Málaga
Keyword(s):  
Bifurcation Diagram ◽  
Limit Cycle ◽  
Excellent Agreement ◽  
Big Bang ◽  
Wide Range ◽  
Coupling Time ◽  
First Time ◽  
Hydrodynamic Oscillator ◽  
Range Of Values ◽  
Theoretical Results

The Tantalus Oscillator is a nonlinear hydrodynamic oscillator with an attractive limit cycle. In this study, we pursue the construction of a biparametric bifurcation diagram for the Tantalus Oscillator under biphasic perturbations. That is the first time that this kind of diagram is built for this kind of oscillator under biphasic perturbations. Results show that biphasic perturbations have no effect when the coupling time is chosen over a wide range of values. This modifies the bifurcation diagram obtained under monophasic perturbations. Now we have the appearance of periodic increment Big Bang Bifurcations. The theoretical results are in excellent agreement with experimental observations.

CHAOTIC COEXISTENCE IN A RESOURCE–CONSUMER MODEL

2019 ◽  
Vol 27 (02) ◽  
pp. 167-184
Author(s):  
DENIS G. LADEIRA ◽  
MARCELO M. de OLIVEIRA
Keyword(s):  
Lyapunov Exponents ◽  
Limit Cycle ◽  
Food Supply ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Dynamic Variable ◽  
Interspecies Competition ◽  
Successive Period ◽  
Consumer Model ◽  
Rate Of Consumption

We study the interspecies competition in a simple resource–consumer model which includes the resource supply as a dynamic variable. In the model, an organism of each species needs to consume a certain minimum rate of resource (food) to survive; a higher rate of consumption is required for reproduction. We analyze the orbit diagrams and Lyapunov exponents in order to characterize the system dynamical behavior. We observe that under a periodic food supply, the system can exhibit coexistence in the form of limit cycle oscillations. For a certain parameter range, we observe chaotic behavior emerging from successive period doublings and quasi-periodicity.

scholarly journals The dynamics of nutrient, toxic phytoplankton, nontoxic phytoplankton and zooplankton model

2016 ◽  
Vol 5 (1) ◽  
pp. 48
Author(s):  
Hasnaa Fiesal Mohammed Hussien ◽  
Raid Kamel Naji ◽  
Azhar Abbas Majeed
Keyword(s):  
Food Web ◽  
Nonlinear Differential Equations ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Toxic Substance ◽  
Global Dynamics ◽  
Defensive Strategy ◽  
Toxic Phytoplankton ◽  
System A ◽  
Aquatic Food

<p>The objective of this paper is to study the dynamical behavior of an aquatic food web system. A mathematical model that includes nutrients, phytoplankton and zooplankton is proposed and analyzed. It is assumed that, the phytoplankton divided into two compartments namely toxic phytoplankton which produces a toxic substance as a defensive strategy against predation by zooplankton, and a nontoxic phytoplankton. All the feeding processes in this food web are formulating according to the Lotka-Volterra functional response. This model is represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global stability conditions of all possible equilibrium points are established. The occurrence of local bifurcation and Hopf bifurcation are investigated. Finally, numerical simulation is used to study the global dynamics of this model.</p>

Limit Cycle‐Strange Attractor Competition

2003 ◽  
Vol 112 (2) ◽  
pp. 133-160 ◽  
Author(s):  
W. O. Criminale ◽  
T. L. Jackson ◽  
P. W. Nelson
Keyword(s):  
Limit Cycle ◽  
Strange Attractor
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