Dynamical Analysis of Coupled Bidirectional FitzHugh–Nagumo Neuronal Networks With Multiple Delays

2019 ◽  
Vol 14 (6) ◽  
Author(s):  
Xiaochen Mao ◽  
Xiangyu Zhou ◽  
Tiantian Shi ◽  
Lei Qiao
Keyword(s):  
Neuronal Networks ◽  
Electronic Circuit ◽  
Dynamical Analysis ◽  
Chaotic Attractors ◽  
Multiple Delays ◽  
Coexisting Attractors ◽  
Science And Engineering ◽  
Chaotic Motions ◽  
Dynamical Behaviors ◽  
Circuit Simulations

Coupled neuronal networks have received considerable attention due to their important and extensive applications in science and engineering. This paper focuses on the nonlinear dynamics of delay-coupled bidirectional FitzHugh–Nagumo (FHN) neuronal networks through theoretical analysis, numerical computations, and circuit simulations. A variety of interesting dynamical behaviors of the network are explored, such as the coexistence of nontrivial equilibria and periodic solutions, different patterns of coexisting attractors, and even chaotic motions. An electronic circuit is designed and performed to validate the facticity of the complicated behaviors, such as multistability and chaotic attractors. It is shown that the circuit simulations reach an agreement with the obtained results.

scholarly journals Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xia Huang ◽  
Zhen Wang ◽  
Yuxia Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Hopfield Neural Network ◽  
Hopfield Neural Networks ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Motions ◽  
Dynamical Behaviors ◽  
Nonlinear Dynamics And Chaos

A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.

Various Attractors, Coexisting Attractors and Antimonotonicity in a Simple Fourth-Order Memristive Twin-T Oscillator

2018 ◽  
Vol 28 (04) ◽  
pp. 1850050 ◽  
Author(s):  
Ling Zhou ◽  
Chunhua Wang ◽  
Xin Zhang ◽  
Wei Yao
Keyword(s):  
Fourth Order ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Random Bit Generator ◽  
In Series ◽  
Dynamical Features

By replacing the resistor in a Twin-T network with a generalized flux-controlled memristor, this paper proposes a simple fourth-order memristive Twin-T oscillator. Rich dynamical behaviors can be observed in the dynamical system. The most striking feature is that this system has various periodic orbits and various chaotic attractors generated by adjusting parameter [Formula: see text]. At the same time, coexisting attractors and antimonotonicity are also detected (especially, two full Feigenbaum remerging trees in series are observed in such autonomous chaotic systems). Their dynamical features are analyzed by phase portraits, Lyapunov exponents, bifurcation diagrams and basin of attraction. Moreover, hardware experiments on a breadboard are carried out. Experimental measurements are in accordance with the simulation results. Finally, a multi-channel random bit generator is designed for encryption applications. Numerical results illustrate the usefulness of the random bit generator.

DYNAMICAL ANALYSIS OF A CHAOTIC SYSTEM WITH TWO DOUBLE-SCROLL CHAOTIC ATTRACTORS

2004 ◽  
Vol 14 (03) ◽  
pp. 971-998 ◽  
Author(s):  
WENBO LIU ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Dynamical Analysis ◽  
Chaotic Attractors ◽  
Compound Structure ◽  
Numerical Examples ◽  
Routes To Chaos ◽  
Basic Properties ◽  
Dynamical Behaviors

Dynamical behaviors of a three-dimensional autonomous chaotic system with two double-scroll attractors are studied. Some basic properties such as bifurcation, routes to chaos, periodic windows and compound structure are demonstrated with various numerical examples. System equilibria and their stabilities are discussed, and chaotic features of the attractors are justified numerically.

scholarly journals Hidden Multistability in a Memristor-Based Cellular Neural Network

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Birong Xu ◽  
Hairong Lin ◽  
Guangyi Wang
Keyword(s):  
Neural Network ◽  
Simulation Analysis ◽  
Equilibrium Points ◽  
Cellular Neural Network ◽  
Nonlinear Phenomena ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Dynamical Behaviors ◽  
Circuit Simulations

In this paper, we report a novel memristor-based cellular neural network (CNN) without equilibrium points. Dynamical behaviors of the memristor-based CNN are investigated by simulation analysis. The results indicate that the system owns complicated nonlinear phenomena, such as hidden attractors, coexisting attractors, and initial boosting behaviors of position and amplitude. Furthermore, both heterogeneous multistability and homogenous multistability are found in the CNN. Finally, Multisim circuit simulations are performed to prove the chaotic characteristics and multistability of the system.

scholarly journals A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Duy Vo Hoang ◽  
Sifeu Takougang Kingni ◽  
Viet-Thanh Pham
Keyword(s):  
Fractional Order ◽  
Chaotic Behavior ◽  
Chaotic Attractors ◽  
Dimensional System ◽  
Hyperchaotic System ◽  
Equilibrium System ◽  
Coexisting Attractors ◽  
Amplitude Control ◽  
Dynamical Behaviors ◽  
Point Attractor

No-equilibrium system with chaotic behavior has attracted considerable attention recently because of its hidden attractor. We study a new four-dimensional system without equilibrium in this work. The new no-equilibrium system exhibits hyperchaos and coexisting attractors. Amplitude control feature of the system is also discovered. The commensurate fractional-order version of the proposed system is studied using numerical simulations. By tuning the commensurate fractional-order, the proposed system displays a wide variety of dynamical behaviors ranging from coexistence of quasiperiodic and chaotic attractors and bistable chaotic attractors to point attractor via transient chaos.

A novel 4D chaotic system with multistability: Dynamical analysis, circuit implementation, control design

2019 ◽  
Vol 33 (21) ◽  
pp. 1950240 ◽  
Author(s):  
Jian-Jun He ◽  
Bang-Cheng Lai
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Electronic Circuit ◽  
Period Doubling ◽  
Control Design ◽  
Critical Value ◽  
Dynamical Analysis ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
The Novel

The purpose of this work is to introduce a novel 4D chaotic system and investigate its multistability. The novel system has an unstable origin and two stable symmetrical hyperbolic equilibria. When the parameter increases across a critical value, the equilibria lose their stability and double Hopf bifurcations occur with the appearance of limit cycles. A pair of point, periodic, chaotic attractors are observed in the system from different initial values for given parameters. The chaos of the system is yielded via period-doubling bifurcation. A double-scroll chaotic attractor is numerically observed as well. By using the electronic circuit, the chaotic attractor of the system is realized. The control problem of the system is reported. An effective controller is designed to stabilize the system.

EXPERIMENTAL BIFURCATIONS OF AN IMPACT OSCILLATOR WITH SMA CONSTRAINT

2012 ◽  
Vol 22 (05) ◽  
pp. 1230017 ◽  
Author(s):  
ELENA SITNIKOVA ◽  
EKATERINA PAVLOVSKAIA ◽  
JAMES ING ◽  
MARIAN WIERCIGROCH
Keyword(s):  
Excitation Frequency ◽  
Dynamic Responses ◽  
Hysteretic Behavior ◽  
Resonance Structure ◽  
Chaotic Attractors ◽  
Coexisting Attractors ◽  
Impact Oscillator ◽  
Restoring Force ◽  
Chaotic Motions ◽  
Highly Nonlinear

In this paper we study bifurcations of an impact oscillator with one sided SMA motion constraint. The excitation frequency is used as a bifurcation parameter and two different values of the excitation amplitude are considered. It is shown that as frequency varies, the system exhibits highly nonlinear behavior. A typical bifurcation diagram has a number of resonance regions separated by chaotic motions with additional windows of periodic responses. The evolution of chaotic attractors is recorded experimentally, and changes in the structure of the attractors are shown. A mathematical model is developed and the results of the simulations are compared with the experimental findings. It is shown that the model is capable of accurately predicting not only the resonance structure but also the shape of the periodic and chaotic attractors. Numerical investigations also reveal a number of coexisting attractors at some frequency values. In particular, three attractors are found numerically for A = 0.2 mm and f = 29.474 Hz and their basins of attraction are presented. For A = 0.2 mm and f = 33.463 Hz , four coexisting attractors are found. For both parameter sets, one of the numerically detected attractors was validated experimentally. The undertaken analysis has shown that the hysteretic behavior of the restraint affected the dynamic responses only at the resonances, when the displacements are sufficiently large to trigger phase transformations in the SMA restraint. In nonresonant frequency ranges the restoring force in the SMA constraint is elastic. These findings are consistent with the numerical analysis carried out in [Sitnikova et al., 2008] for a similar system, which showed that the hysteretic behavior of the SMA affects resonant responses and provides a substantial vibration reduction in those regions.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

Dynamical Analysis of bantam-Regulated Drosophila Circadian Rhythm Model

2014 ◽  
Vol 24 (12) ◽  
pp. 1450161 ◽  
Author(s):  
Ying Li ◽  
Zengrong Liu
Keyword(s):  
Circadian Rhythm ◽  
Crucial Role ◽  
Target Genes ◽  
Classical Model ◽  
Dynamical Analysis ◽  
Biological Processes ◽  
Biological Mechanisms ◽  
Environmental Perturbations ◽  
Dynamical Behaviors ◽  
Important Regulator

MicroRNAs (miRNAs) interact with 3′untranslated region (UTR) elements of target genes to regulate mRNA stability or translation, and play a crucial role in regulating many different biological processes. bantam, a conserved miRNA, is involved in several functions, such as regulating Drosophila growth and circadian rhythm. Recently, it has been discovered that bantam plays a crucial role in the core circadian pacemaker. In this paper, based on experimental observations, a detailed dynamical model of bantam-regulated circadian clock system is developed to show the post-transcriptional behaviors in the modulation of Drosophila circadian rhythm, in which the regulation of bantam is incorporated into a classical model. The dynamical behaviors of the model are consistent with the experimental observations, which shows that bantam is an important regulator of Drosophila circadian rhythm. The sensitivity analysis of parameters demonstrates that with the regulation of bantam the system is more sensitive to perturbations, indicating that bantam regulation makes it easier for the organism to modulate its period against the environmental perturbations. The effectiveness in rescuing locomotor activity rhythms of mutated flies shows that bantam is necessary for strong and sustained rhythms. In addition, the biological mechanisms of bantam regulation are analyzed, which may help us more clearly understand Drosophila circadian rhythm regulated by other miRNAs.

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