scholarly journals Analysis, Synchronization, and Robotic Application of a Modified Hyperjerk Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Lazaros Moysis ◽  
Eleftherios Petavratzis ◽  
Muhammad Marwan ◽  
Christos Volos ◽  
Hector Nistazakis ◽  
...  
Keyword(s):  
Chaos Theory ◽  
Nonlinear Term ◽  
Dynamical Analysis ◽  
Coexisting Attractors ◽  
Hyperbolic Sine ◽  
Route To Chaos ◽  
Hyperjerk System ◽  
Parameter Values ◽  
Robotic Application ◽  
Hyperbolic Sine Function

In this work, a novel hyperjerk system, with hyperbolic sine function as the only nonlinear term, is proposed, as a modification of a hyperjerk system proposed by Leutcho et al. First, a dynamical analysis on the system is performed and interesting phenomena concerning chaos theory, such as route to chaos, antimonotonicity, crisis, and coexisting attractors, are studied. For this reason, the system’s bifurcation diagrams with respect to different parameter values are plotted and its Lyapunov exponents are computed. Afterwards, the synchronization of the system is considered, using active control. The proposed system is then applied, as a chaotic generator, to the problem of chaotic path planning, using a combination of sampling and a modulo tactic technique.

scholarly journals A Novel Autonomous 5-D Hyperjerk RC Circuit with Hyperbolic Sine Function

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
N. Tsafack ◽  
J. Kengne
Keyword(s):  
Complex Dynamics ◽  
Dynamical Behavior ◽  
Sine Function ◽  
Coexisting Attractors ◽  
Initial State ◽  
Nonlinear Part ◽  
Hyperbolic Sine ◽  
Rc Circuit ◽  
Hyperjerk System ◽  
Hyperbolic Sine Function

A novel autonomous 5-D hyperjerk RC circuit with hyperbolic sine function is proposed in this paper. Compared to some existing 5-D systems like the 5-D Sprott B system, the 5-D Lorentz, and the Lorentz-like systems, the new system is the simplest 5-D system with complex dynamics reported to date. Its simplicity mainly relies on its nonlinear part which is synthetized using only two semiconductor diodes. The system displays only one equilibrium point and can exhibit both periodic and chaotic dynamical behavior. The complex dynamics of the system is investigated by means of bifurcation analysis. In particular, the striking phenomenon of multistability is revealed showing up to seven coexisting attractors in phase space depending solely on the system’s initial state. To the best of author’s knowledge, this rich dynamics has not yet been revealed in any 5-D dynamical system in general or particularly in any hyperjerk system. Pspice circuit simulations are performed to verify theoretical/numerical analysis.

scholarly journals Circuit Implementation of a Modified Chaotic System with Hyperbolic Sine Nonlinearities Using Bi-Color LED

Technologies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 15
Author(s):  
Christos K. Volos ◽  
Lazaros Moysis ◽  
George D. Roumelas ◽  
Aggelos Giakoumis ◽  
Hector E. Nistazakis ◽  
...  
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Original System ◽  
Dynamical Analysis ◽  
Phase Portraits ◽  
Circuit Realization ◽  
Hyperbolic Sine ◽  
Route To Chaos ◽  
Sine Functions

In this paper, a chaotic three dimansional dynamical system is proposed, that is a modification of the system in Volos et al. (2017). The new system has two hyperbolic sine nonlinear terms, as opposed to the original system that only included one, in order to optimize system’s chaotic behavior, which is confirmed by the calculation of the maximal Lyapunov exponents and Kaplan-Yorke dimension. The system is experimentally realized, using Bi-color LEDs to emulate the hyperbolic sine functions. An extended dynamical analysis is then performed, by computing numerically the system’s bifurcation and continuation diagrams, Lyapunov exponents and phase portraits, and comparing the numerical simulations with the circuit simulations. A series of interesting phenomena are unmasked, like period doubling route to chaos, coexisting attractors and antimonotonicity, which are all verified from the circuit realization of the system. Hence, the circuit setup accurately emulates the chaotic dynamics of the proposed system.

A Dream that has Come True: Chaos from a Nonlinear Circuit with a Real Memristor

2020 ◽  
Vol 30 (13) ◽  
pp. 2030036
Author(s):  
Christos K. Volos ◽  
Viet-Thanh Pham ◽  
Hector E. Nistazakis ◽  
Ioannis N. Stouboulos
Keyword(s):  
Chaos Theory ◽  
Period Doubling ◽  
Nonlinear Circuits ◽  
Nonlinear Element ◽  
Chaotic Attractors ◽  
Nonlinear Circuit ◽  
Coexisting Attractors ◽  
Circuit Element ◽  
Route To Chaos ◽  
First Time

In the last decade, researchers, who work in the field of nonlinear circuits, have the “dream” to use a real memristor, which is the only nonlinear fundamental circuit element, in a new or other reported nonlinear circuit in literature, in order to experimentally investigate chaos. With this intention, for the first time, a well-known nonlinear circuit, in which its nonlinear element has been replaced with a commercially available memristor (KNOWM memristor), is presented in this work. Interesting phenomena concerning chaos theory, such as period-doubling route to chaos, coexisting attractors, one-scroll and double-scroll chaotic attractors are experimentally observed.

Transitions Through Period Doubling Route to Chaos

1991 ◽  
Author(s):  
R. M. Evan-lwanowski ◽  
Chu-Ho Lu
Keyword(s):  
Period Doubling ◽  
Mirror Image ◽  
Flip Flop ◽  
Physical Systems ◽  
Starting Conditions ◽  
Spatial System ◽  
Stationary Bifurcation ◽  
Extreme Sensitivity ◽  
Route To Chaos ◽  
Parameter Values

Abstract The Duffing driven, damped, “softening” oscillator has been analyzed for transition through period doubling route to chaos. The forcing frequency and amplitude have been varied in time (constant sweep). The stationary 2T, 4T… chaos regions have been determined and used as the starting conditions for nonstationary regimes, consisting of the transition along the Ω(t)=Ω0±α2t,f=const., Ω-line, and along the E-line: Ω(t)=Ω0±α2t;f(t)=f0∓α2t. The results are new, revealing, puzzling and complex. The nonstationary penetration phenomena (delay, memory) has been observed for a single and two-control nonstationary parameters. The rate of penetrations tends to zero with increasing sweeps, delaying thus the nonstationary chaos relative to the stationary chaos by a constant value. A bifurcation discontinuity has been uncovered at the stationary 2T bifurcation: the 2T bifurcation discontinuity drops from the upper branches of (a, Ω) or (a, f) curves to their lower branches. The bifurcation drops occur at the different control parameter values from the response x(t) discontinuities. The stationary bifurcation discontinuities are annihilated in the nonstationary bifurcation cascade to chaos — they reside entirely on the upper or lower nonstationary branches. A puzzling drop (jump) of the chaotic bifurcation bands has been observed for reversed sweeps. Extreme sensitivity of the nonstationary bifurcations to the starting conditions manifests itself in the flip-flop (mirror image) phenomena. The knowledge of the bifurcations allows for accurate reconstruction of the spatial system itself. The results obtained may model mathematically a number of engineering and physical systems.

scholarly journals Dynamical analysis and FPGA implementation of a large range chaotic system with coexisting attractors

2018 ◽  
Vol 11 ◽  
pp. 368-376 ◽  
Author(s):  
Yong-ju Xian ◽  
Cheng Xia ◽  
Tao-tao Guo ◽  
Kun-rong Fu ◽  
Chang-biao Xu
Keyword(s):  
Chaotic System ◽  
Large Range ◽  
Fpga Implementation ◽  
Dynamical Analysis ◽  
Coexisting Attractors

CHAOTIC DYNAMICS OF A SIMPLE PARAMETRICALLY DRIVEN DISSIPATIVE CIRCUIT

2011 ◽  
Vol 21 (07) ◽  
pp. 1927-1933 ◽  
Author(s):  
P. PHILOMINATHAN ◽  
M. SANTHIAH ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
S. RAJASEKAR
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponents ◽  
Chaotic Dynamics ◽  
Period Doubling ◽  
Classic Period ◽  
Control Signal ◽  
Period Doubling Bifurcation ◽  
Chaotic Circuit ◽  
Route To Chaos ◽  
Parameter Values

We introduce a simple parametrically driven dissipative second-order chaotic circuit. In this circuit, one of the circuit parameters is varied by an external periodic control signal. Thus by tuning the parameter values of this circuit, classic period-doubling bifurcation route to chaos is found to occur. The experimentally observed phenomena is further validated through corresponding numerical simulation of the circuit equations. The periodic and chaotic dynamics of this model is further characterized by computing Lyapunov exponents.

Hot workability of V-Ti microalloyed steel for forging

2019 ◽  
Vol 116 (2) ◽  
pp. 216 ◽  
Author(s):  
Ningbo Zhou ◽  
Fan Zhao ◽  
Meng Wu ◽  
Bo Jiang ◽  
Chaolei Zhang ◽  
...  
Keyword(s):  
Microalloyed Steel ◽  
True Strain ◽  
The Other ◽  
Strain Rates ◽  
Hot Workability ◽  
Hollomon Parameter ◽  
Hyperbolic Sine ◽  
Reduction Of Area ◽  
The Relationship ◽  
Hyperbolic Sine Function

The hot compression and the hot tensile experiments were carried out on a Gleeble3800 thermal-mechanical simulator at different deformation conditions. The relationship between the flow stress and Zener-Hollomon parameter was established by the hyperbolic sine function. The hot deformation apparent activation energy is about 371 kJ/mol. There are two peak regions of m-value in the m maps with true strain of 0.2. One peak corresponds to the temperature of 1050 °C and the strain rate of 0.01 s−1, the other one corresponds to the temperature of 1200 °C and the strain rates within range of 0.1 s−1 ∼ 1 s−1. There is only one peak region (1150 °C ∼ 1200 °C, 0.1 s−1 ∼ 1 s−1) of m-value, when true strain is 0.4 or 0.9. The reduction of area increases from 65% to 98% with the temperature increases from 800 °C to 1200 °C. In temperature range of 1000 °C ∼ 1200 °C, the reduction of area is always over 90%, which means that the plasticity of the steel is fine. According to the results of the research, it can be proved that the optimal deformation conditions with different strain correspond to the peak regions of m-value. The optimum deformation conditions is the temperature of 1200 °C and the strain rates within range of 0.1 s−1 ∼ 1 s−1, which were suitable for the true strain with 0.2, 0.4 and 0.9 at the same time.

scholarly journals Mathematical Model for Small Size Time Series Data of Bacterial Secondary Metabolic Pathways

2018 ◽  
Vol 12 ◽  
pp. 117793221877507 ◽  
Author(s):  
Daisuke Tominaga ◽  
Hideo Kawaguchi ◽  
Yoshimi Hori ◽  
Tomohisa Hasunuma ◽  
Chiaki Ogino ◽  
...  
Keyword(s):  
Metabolic Pathways ◽  
Time Series Data ◽  
Reaction Pathway ◽  
Lactate Production ◽  
Reaction Rates ◽  
Small Sample ◽  
Dynamical Analysis ◽  
Series Data ◽  
Sufficient Information ◽  
Parameter Values

Measuring the concentrations of metabolites and estimating the reaction rates of each reaction step consisting of metabolic pathways are significant for an improvement in microorganisms used in maximizing the production of materials. Although the reaction pathway must be identified for such an improvement, doing so is not easy. Numerous reaction steps have been reported; however, the actual reaction steps activated vary or change according to the conditions. Furthermore, to build mathematical models for a dynamical analysis, the reaction mechanisms and parameter values must be known; however, to date, sufficient information has yet to be published for many cases. In addition, experimental observations are expensive. A new mathematical approach that is applicable to small sample data, and that requires no detailed reaction information, is strongly needed. S-system is one such model that can use smaller samples than other ordinary differential equation models. We propose a simplified S-system to apply minimal quantities of samples for a dynamic analysis of the metabolic pathways. We applied the model to the phenyl lactate production pathway of Escherichia coli. The model obtained suggests that actually activated reaction steps and feedback are inhibitions within the pathway.

Sign in / Sign up

Export Citation Format

Share Document