scholarly journals Dynamic Analysis of a Particle Motion System

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 7
Author(s):  
Ning Cui ◽  
Junhong Li
Keyword(s):  
Particle Motion ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Equilibrium Stability ◽  
Dynamic Behaviors ◽  
Motion System ◽  
The Rich ◽  
Theoretical Analyses

This paper formulates a new particle motion system. The dynamic behaviors of the system are studied including the continuous dependence on initial conditions of the system’s solution, the equilibrium stability, Hopf bifurcation at the equilibrium point, etc. This shows the rich dynamic behaviors of the system, including the supercritical Hopf bifurcations, subcritical Hopf bifurcations, and chaotic attractors. Numerical simulations are carried out to verify theoretical analyses and to exhibit the rich dynamic behaviors.

A new hyperchaotic particle motion system and its control

2019 ◽  
Vol 30 (12) ◽  
pp. 2050004
Author(s):  
Ning Cui ◽  
Junhong Li
Keyword(s):  
Particle Motion ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Multiple Equilibrium ◽  
Hopf Bifurcations ◽  
Hyperchaotic System ◽  
Motion System ◽  
The Rich ◽  
Theoretical Analyses ◽  
Multiple Equilibrium Points

This paper formulates a new hyperchaotic system for particle motion. The continuous dependence on initial conditions of the system’s solution and the equilibrium stability, bifurcation, energy function of the system are analyzed. The hyperchaotic behaviors in the motion of the particle on a horizontal smooth plane are also investigated. It shows that the rich dynamic behaviors of the system, including the degenerate Hopf bifurcations and nondegenerate Hopf bifurcations at multiple equilibrium points, the irregular variation of Hamiltonian energy, and the hyperchaotic attractors. These results generalize and improve some known results about the particle motion system. Furthermore, the constraint of hyperchaos control is obtained by applying Lagrange’s method and the constraint change the system from a hyperchaotic state to asymptotically state. The numerical simulations are carried out to verify theoretical analyses and to exhibit the rich hyperchaotic behaviors.

scholarly journals Dynamic Behaviors Analysis of a Chaotic Circuit Based on a Novel Fractional-Order Generalized Memristor

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Ningning Yang ◽  
Shucan Cheng ◽  
Chaojun Wu ◽  
Rong Jia ◽  
Chongxin Liu
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Chaotic Attractors ◽  
Chaotic Circuit ◽  
Diagram Method ◽  
Dynamic Behaviors ◽  
System Parameters ◽  
Pinched Hysteresis Loop ◽  
The Impact ◽  
The Mathematical Model

In this paper, a fractional-order chaotic circuit based on a novel fractional-order generalized memristor is proposed. It is proved that the circuit based on the diode bridge cascaded with fractional-order inductor has volt-ampere characteristics of pinched hysteresis loop. Then the mathematical model of the fractional-order memristor chaotic circuit is obtained. The impact of the order and system parameters on the dynamic behaviors of the chaotic circuit is studied by phase trajectory, Poincaré Section, and bifurcation diagram method. The order, as an important parameter, can increase the degree of freedom of the system. With the change of the order and parameters, the circuit will exhibit abundant dynamic behaviors such as coexisting upper and lower limit cycle, single scroll chaotic attractors, and double scroll chaotic attractors under different initial conditions. And the system exhibits antimonotonic behavior of antiperiodic bifurcation with the change of system parameters. The equivalent circuit simulations are designed to verify the results of the theoretical analysis and numerical simulation.

A MODIFIED GENERALIZED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM

2009 ◽  
Vol 19 (06) ◽  
pp. 1931-1949 ◽  
Author(s):  
QIGUI YANG ◽  
KANGMING ZHANG ◽  
GUANRONG CHEN
Keyword(s):  
Special Form ◽  
Topological Structure ◽  
Complex Dynamics ◽  
Type System ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Compound Structure ◽  
Two Parameters ◽  
First Time ◽  
New System

In this paper, a modified generalized Lorenz-type system is introduced, which is state-equivalent to a simple and special form, and is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, two classes of new chaotic attractors are found for the first time in the literature, which are similar but nonequivalent in topological structure. To further understand the complex dynamics of the new system, some basic properties such as Lyapunov exponents, Hopf bifurcations and compound structure of the attractors are analyzed and demonstrated with careful numerical simulations.

scholarly journals Dependence on the Initial Data for the Continuous Thermostatted Framework

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 602
Author(s):  
Bruno Carbonaro ◽  
Marco Menale
Keyword(s):  
Complex System ◽  
Initial Data ◽  
External Force ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Complete Information ◽  
Complete Picture ◽  
Order Moment ◽  
Lack Of Information ◽  
Activity Variable

The paper deals with the problem of continuous dependence on initial data of solutions to the equation describing the evolution of a complex system in the presence of an external force acting on the system and of a thermostat, simply identified with the condition that the second order moment of the activity variable (see Section 1) is a constant. We are able to prove that these solutions are stable with respect to the initial conditions in the Hadamard’s sense. In this connection, two remarks spontaneously arise and must be carefully considered: first, one could complain the lack of information about the “distance” between solutions at any time t ∈ [ 0 , + ∞ ) ; next, one cannot expect any more complete information without taking into account the possible distribution of the transition probabiliy densities and the interaction rates (see Section 1 again). This work must be viewed as a first step of a research which will require many more steps to give a sufficiently complete picture of the relations between solutions (see Section 5).

scholarly journals Infinitely Many Coexisting Attractors in No-Equilibrium Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Qiang Lai ◽  
Paul Didier Kamdem Kuate ◽  
Huiqin Pei ◽  
Hilaire Fotsin
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Physical Meaning ◽  
Control Method ◽  
Initial Conditions ◽  
Periodic Motions ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Dynamic Behaviors

This paper proposes a new no-equilibrium chaotic system that has the ability to yield infinitely many coexisting hidden attractors. Dynamic behaviors of the system with respect to the parameters and initial conditions are numerically studied. It shows that the system has chaotic, quasiperiodic, and periodic motions for different parameters and coexists with a large number of hidden attractors for different initial conditions. The circuit and microcontroller implementations of the system are given for illustrating its physical meaning. Also, the synchronization conditions of the system are established based on the adaptive control method.

STOCK-HARVEST DYNAMICS IN MULTIAGENT FISHERIES

2011 ◽  
Vol 21 (01) ◽  
pp. 363-372
Author(s):  
EN-GUO GU
Keyword(s):  
Initial Conditions ◽  
Profit Maximization ◽  
Fish Stock ◽  
Maximization Problem ◽  
Chaotic Attractors ◽  
Two Dimensional ◽  
Fishery Resource ◽  
Global Dynamic ◽  
Existence And Stability ◽  
Fishery Model

In this work, we build a two-dimensional dynamical fishery model in which the total harvest is obtained by a multiagent game with best reply strategy and naive expectations, i.e. each agent decides the harvest quantity by solving a profit maximization problem. Special attention is paid to the global dynamic analysis in the light of feasible domains (initial conditions giving non-negative trajectories converging to an equilibrium), which is related to the crisis of extinction. We also study the existence and stability of non-negative equilibria for models through mathematical analysis and numerical simulations. We discover the increase in the margin price of fish stock may lead to instability of the fixed point and make the system sink into chaotic attractors. Thus the fishery resource may fluctuate in a stochastic form.

New Approach of the Playfair's Cipher with A Numerical Value of the Keyword

2017 ◽  
Vol 6 (3) ◽  
pp. 695 ◽  
Author(s):  
Assia Merzoug ◽  
Adda Ali-Pacha ◽  
Naima Hadj-Said
Keyword(s):  
Chaotic Maps ◽  
Initial Conditions ◽  
Logistic Map ◽  
Academic Research ◽  
Chaotic Attractors ◽  
New Approach ◽  
Single Character ◽  
Dimension 2

<p>At least during the last five years there has been an explosion of a public academic research in cryptography for Playfair's cipher. We were interested, and we have proposed a method to improve it, to make it safer and more efficient. We have oversized this encryption matrix by 7x7 coefficents and for its filling, we have combined two chaotic maps (the attractor Henon and logistics map). The attractor Henon of dimension 2, determines the intersection of the row and column of the new matrix playfair. The coefficients of this matrix are calculated from logistic map, each value is a single character of the alphabet used. The secret keyword is formed by the initial conditions of the chaotic attractors.</p>

scholarly journals Experimentally Accessible Orbits Near a Bykov Cycle

2020 ◽  
Vol 30 (10) ◽  
pp. 2030030
Author(s):  
Roberto Barrio ◽  
Maria Carvalho ◽  
Luísa Castro ◽  
Alexandre A. P. Rodrigues
Keyword(s):  
Chaotic Dynamics ◽  
Vector Fields ◽  
Initial Conditions ◽  
Parabolic Type ◽  
Chaotic Attractors ◽  
Heteroclinic Cycle ◽  
Type Curves ◽  
Local And Global Bifurcations ◽  
Domain Of Parameters ◽  
Two Parameter

This paper reports numerical experiments done on a two-parameter family of vector fields which unfold an attracting heteroclinic cycle linking two saddle-foci. We investigated both local and global bifurcations due to symmetry breaking in order to detect either hyperbolic or chaotic dynamics. Although a complete understanding of the corresponding bifurcation diagram and the mechanisms underlying the dynamical changes is still out of reach, using a combination of theoretical tools and computer simulations we have uncovered some complex patterns. We have selected suitable initial conditions to analyze the bifurcation diagrams, and regarding these solutions we have located: (a) an open domain of parameters with regular dynamics; (b) infinitely many parabolic-type curves associated to homoclinic Shilnikov cycles which act as organizing centers; (c) a crisis region related to the destruction or creation of chaotic attractors; (d) a large Lebesgue measure set of parameters where chaotic regimes are dominant, though sinks and chaotic attractors may coexist, and in whose complement we observe shrimps.

scholarly journals On a class of nonclassical hyperbolic equations with nonlocal conditions

2002 ◽  
Vol 15 (2) ◽  
pp. 125-140 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Continuous Dependence ◽  
Hyperbolic Equations ◽  
Initial Conditions ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
A Priori Estimate ◽  
Analysis Method ◽  
Priori Estimate ◽  
Abstract Formulation

This paper proves the existence, uniqueness and continuous dependence of a solution of a class of nonclassical hyperbolic equations with nonlocal boundary and initial conditions. Results are obtained by using a functional analysis method based on an a priori estimate and on the density of the range of the linear operator corresponding to the abstract formulation of the considered problem.

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