Complex Dynamics in a Memristive Diode Bridge-Based MLC Circuit: Coexisting Attractors and Double-Transient Chaos

2021 ◽  
Vol 31 (03) ◽  
pp. 2150049
Author(s):  
A. Chithra ◽  
T. Fonzin Fozin ◽  
K. Srinivasan ◽  
E. R. Mache Kengne ◽  
A. Tchagna Kouanou ◽  
...  
Keyword(s):  
Complex Dynamics ◽  
Basin Of Attraction ◽  
Period Doubling ◽  
Transient Chaos ◽  
Multiple Attractors ◽  
Simulation Tools ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Crisis Scenarios ◽  
Complex Phenomena

This paper uncovers some striking and new complex phenomena in a memristive diode bridge-based Murali–Lakshmanan–Chua (MLC) circuit. These striking dynamical behaviors include the coexistence of multiple attractors and double-transient chaos. Also, period-doubling, chaos, crisis scenarios are observed in the system when varying the amplitude of the external excitation. Numerical simulation tools like phase portrait, cross-section basin of attraction, Lyapunov spectrum, bifurcation diagrams and time series are used to highlight the complex dynamical behaviors in the memristive system. Further, practical realizations of the circuit both in PSpice and real-laboratory measurements match well with the observed numerical simulations.

scholarly journals Complex Dynamics of Discrete SEIS Models with Simple Demography

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Hui Cao ◽  
Yicang Zhou ◽  
Baojun Song
Keyword(s):  
Numerical Simulations ◽  
Mathematical Analysis ◽  
Complex Dynamics ◽  
Treatment Strategies ◽  
Period Doubling ◽  
Demographic Factors ◽  
Multiple Attractors ◽  
Equilibrium Dynamics ◽  
Epidemiological Factors ◽  
Dynamical Behaviors

We investigate bifurcations and dynamical behaviors of discrete SEIS models with exogenous reinfections and a variety of treatment strategies. Bifurcations identified from the models include period doubling, backward, forward-backward, and multiple backward bifurcations. Multiple attractors, such as bistability and tristability, are observed. We also estimate the ultimate boundary of the infected regardless of initial status. Our rigorously mathematical analysis together with numerical simulations show that epidemiological factors alone can generate complex dynamics, though demographic factors only support simple equilibrium dynamics. Our model analysis supports and urges to treat a fixed percentage of exposed individuals.

scholarly journals Circuit Implementation, Synchronization of Multistability, and Image Encryption of a Four-Wing Memristive Chaotic System

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Guangya Peng ◽  
Fuhong Min ◽  
Enrong Wang
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Secure Communication ◽  
Secret Key ◽  
Multiple Attractors ◽  
Dynamical Behaviors ◽  
Key Space ◽  
Control Scheme ◽  
Memristive System ◽  
Coexistence Of Multiple Attractors

The four-wing memristive chaotic system used in synchronization is applied to secure communication which can increase the difficulty of deciphering effectively and enhance the security of information. In this paper, a novel four-wing memristive chaotic system with an active cubic flux-controlled memristor is proposed based on a Lorenz-like circuit. Dynamical behaviors of the memristive system are illustrated in terms of Lyapunov exponents, bifurcation diagrams, coexistence Poincaré maps, coexistence phase diagrams, and attraction basins. Besides, the modular equivalent circuit of four-wing memristive system is designed and the corresponding results are observed to verify its accuracy and rationality. A nonlinear synchronization controller with exponential function is devised to realize synchronization of the coexistence of multiple attractors, and the synchronization control scheme is applied to image encryption to improve secret key space. More interestingly, considering different influence of multistability on encryption, the appropriate key is achieved to enhance the antideciphering ability.

Dynamical Effects of Neuron Activation Gradient on Hopfield Neural Network: Numerical Analyses and Hardware Experiments

2019 ◽  
Vol 29 (04) ◽  
pp. 1930010 ◽  
Author(s):  
Bocheng Bao ◽  
Chengjie Chen ◽  
Han Bao ◽  
Xi Zhang ◽  
Quan Xu ◽  
...  
Keyword(s):  
Neural Network ◽  
Control Parameter ◽  
Period Doubling ◽  
Response Speed ◽  
Hopfield Neural Network ◽  
Activation Function ◽  
Numerical Analyses ◽  
Dynamical Behaviors ◽  
Neuron Activation ◽  
Crisis Scenarios

Hyperbolic tangent function, a bounded monotone differentiable function, is usually taken as a neuron activation function, whose activation gradient, i.e. gain scaling parameter, can reflect the response speed in the neuronal electrical activities. However, the previously published literatures have not yet paid attention to the dynamical effects of the neuron activation gradient on Hopfield neural network (HNN). Taking the neuron activation gradient as an adjustable control parameter, dynamical behaviors with the variation of the control parameter are investigated through stability analyses of the equilibrium states, numerical analyses of the mathematical model, and experimental measurements on a hardware level. The results demonstrate that complex dynamical behaviors associated with the neuron activation gradient emerge in the HNN model, including coexisting limit cycle oscillations, coexisting chaotic spiral attractors, chaotic double scrolls, forward and reverse period-doubling cascades, and crisis scenarios, which are effectively confirmed by neuron activation gradient-dependent local attraction basins and parameter-space plots as well. Additionally, the experimentally measured results have nice consistency to numerical simulations.

Generating Four-Wing Hyperchaotic Attractor and Two-Wing, Three-Wing, and Four-Wing Chaotic Attractors in 4D Memristive System

2017 ◽  
Vol 27 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Ling Zhou ◽  
Chunhua Wang ◽  
Lili Zhou
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Hyperchaotic System ◽  
Multiple Attractors ◽  
System A ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Line Of Equilibria

By adding only one smooth flux-controlled memristor into a three-dimensional (3D) pseudo four-wing chaotic system, a new real four-wing hyperchaotic system is constructed in this paper. It is interesting to see that this new memristive chaotic system can generate a four-wing hyperchaotic attractor with a line of equilibria. Moreover, it can generate two-, three- and four-wing chaotic attractors with the variation of a single parameter which denotes the strength of the memristor. At the same time, various coexisting multiple attractors (e.g. three-wing attractors, four-wing attractors and attractors with state transition under the same system parameters) are observed in this system, which means that extreme multistability arises. The complex dynamical behaviors of the proposed system are analyzed by Lyapunov exponents (LEs), phase portraits, Poincaré maps, and time series. An electronic circuit is finally designed to implement the hyperchaotic memristive system.

BIFURCATION AND CHAOS IN THE TINKERBELL MAP

2011 ◽  
Vol 21 (11) ◽  
pp. 3137-3156 ◽  
Author(s):  
SHAOLIANG YUAN ◽  
TAO JIANG ◽  
ZHUJUN JING
Keyword(s):  
Three Dimensional ◽  
Period Doubling ◽  
Phase Portraits ◽  
Transient Chaos ◽  
Flip Bifurcation ◽  
Maximum Lyapunov Exponent ◽  
Invariant Circle ◽  
Dynamical Behaviors ◽  
Fold Bifurcation ◽  
Period Doubling Bifurcations

In this paper, the dynamical behaviors of the Tinkerbell map are investigated in detail. Conditions for the existence of fold bifurcation, flip bifurcation and Hopf bifurcation are derived, and chaos in the sense of Marotto is verified by both analytical and numerical methods. Numerical simulations include bifurcation diagrams in two- and three-dimensional spaces, phase portraits, and the maximum Lyapunov exponent and fractal dimension, as well as the distribution of dynamics in the parameter plane, which exhibit new and interesting dynamical behaviors. More specifically, this paper reports the findings of chaos in the sense of Marotto, a route from an invariant circle to transient chaos with a great abundance of periodic windows, including period-2, 7, 8, 9, 10, 13, 17, 19, 23, 26 and so on, and suddenly appearing or disappearing chaos, convergence of an invariant circle to a period-one orbit, symmetry-breaking of periodic orbits, interlocking period-doubling bifurcations in chaotic regions, interior crisis, chaotic attractors, coexisting (2, 10, 13) chaotic sets, two coexisting invariant circles, two attracting chaotic sets coexisting with a non-attracting chaotic set, and so on, all in the Tinkerbell map. In particular, it is found that there is no obvious road from period-doubling bifurcations to chaos, but there is a route from a period-one orbit to an invariant circle and then to transient chaos as the parameters are varied. Combining the existing results in the current literature with the new results reported in this paper, a more complete understanding of the Tinkerbell map is obtained.

The Design and Realization of a Hyper-Chaotic Circuit Based on a Flux-Controlled Memristor with Linear Memductance

2017 ◽  
Vol 27 (03) ◽  
pp. 1850038 ◽  
Author(s):  
Chunhua Wang ◽  
Ling Zhou ◽  
Renping Wu
Keyword(s):  
Chaotic System ◽  
Circuit Simulation ◽  
Piecewise Linear ◽  
Chaotic Circuit ◽  
Multiple Attractors ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Pinched Hysteresis Loop ◽  
The Lorenz System ◽  
Pinched Hysteresis

In this paper, a flux-controlled memristor with linear memductance is proposed. Compared with the memristor with piecewise linear memductance and the memristor with smooth continuous nonlinearity memductance which are widely used in the study of memristive chaotic system, the proposed memristor has simple mathematical model and is easy to implement. Multisim circuit simulation and breadboard experiment are realized, and the memristor can exhibit a pinched hysteresis loop in the voltage–current plane when driven by a periodic voltage. In addition, a new hyper-chaotic system is presented in this paper by adding the proposed memristor into the Lorenz system. The transient chaos and multiple attractors are observed in this memristive system. The dynamical behaviors of the proposed system are analyzed by equilibria, Lyapunov exponents, bifurcation diagram and phase portrait. Finally, an electronic circuit is designed to implement the hyper-chaotic memristive system.

scholarly journals Complex Dynamical Behaviors of a Fractional-Order System Based on a Locally Active Memristor

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Yajuan Yu ◽  
Han Bao ◽  
Min Shi ◽  
Bocheng Bao ◽  
Yangquan Chen ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Hysteresis Loop ◽  
Fractional Order ◽  
Period Doubling ◽  
Order System ◽  
Periodic Signal ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Attraction Basins ◽  
The Stability

A fractional-order locally active memristor is proposed in this paper. When driven by a bipolar periodic signal, the generated hysteresis loop with two intersections is pinched at the origin. The area of the hysteresis loop changes with the fractional order. Based on the fractional-order locally active memristor, a fractional-order memristive system is constructed. The stability analysis is carried out and the stability conditions for three equilibria are listed. The expression of the fractional order related to Hopf bifurcation is given. The complex dynamical behaviors of Hopf bifurcation, period-doubling bifurcation, bistability and chaos are shown numerically. Furthermore, the bistability behaviors of the different fractional order are validated by the attraction basins in the initial value plane. As an alternative to validating our results, the fractional-order memristive system is implemented by utilizing Simulink of MATLAB. The research results clarify that the complex dynamical behaviors are attributed to two facts: one is the fractional order that affects the stability of the equilibria, and the other is the local activeness of the fractional-order memristor.

Extreme Multistability and Complex Dynamics of a Memristor-Based Chaotic System

2020 ◽  
Vol 30 (08) ◽  
pp. 2030019
Author(s):  
Hui Chang ◽  
Yuxia Li ◽  
Guanrong Chen ◽  
Fang Yuan
Keyword(s):  
Complex Dynamics ◽  
Hysteresis Loops ◽  
Digital Signal ◽  
Phase Portraits ◽  
Transient Chaos ◽  
Bifurcation Diagrams ◽  
Extreme Multistability ◽  
Memristive System ◽  
Autonomous Differential Equations ◽  
Pinched Hysteresis

A memristor with coexisting pinched hysteresis loops and twin local activity domains is presented and analyzed, with an emulator being designed and applied to the classic Chua’s circuit to replace the diode. The memristive system is modeled with four coupled first-order autonomous differential equations, which has three equilibria determined by three static equilibria of the memristor but not controlled by the system parameters. The complex dynamics of the system are analyzed by using compound coexisting bifurcation diagrams, Lyapunov exponent spectra and phase portraits, including point attractors, limit cycles, symmetrical chaotic attractors and their blasting, extreme multistability, state-switching without parameter, and transient chaos. Of particular surprise is that the extreme multistability of the system is hidden and symmetrically distributed. It is found that the existence of transient chaos in the specified parameter domain is determined by using bifurcation diagrams within different time durations and Lyapunov exponents with chaotic sequences. Finally, the symmetrical chaotic attractor and the system blasting are verified by digital signal processing experiments, which are consistent with the numerical analysis.

scholarly journals Modelling and Analysis of a Host-Parasitoid Impulsive Ecosystem under Resource Limitation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Peipei Wang ◽  
Wenjie Qin ◽  
Guangyao Tang
Keyword(s):  
Pest Control ◽  
Bifurcation Analysis ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Limited Resource ◽  
Optimal Number ◽  
Theoretical Development ◽  
Multiple Attractors ◽  
Pest Outbreaks ◽  
Impulsive Model

With a long history of theoretical development, biological model has focused on the interaction of a parasitoid and its host. In this paper, two Nicholson-Bailey models with a nonlinear pulse control strategy are proposed and analyzed to examine how limited resource affects the pest control. For a fixed-time discrete impulsive model, the existence and stability of the host-free periodic solution are derived. Threshold analysis suggests that it is critical to release parasitoid in an optimal number in case of the happening of the intra-specific competition, which will seriously affect the pest control. Bifurcation analysis reveals that the model exists complex dynamics including period doubling, chaotic solutions, coexistence of multiple attractors, and so on. For a state-dependent discrete impulsive model, the numerical simulations for bifurcation analysis are studied, the results show that how the key parameters and the initial densities of both populations affect the pest outbreaks, and consequently the relative biological implications with respect to pest control are discussed.

Asymmetry-Induced Dynamics for a Class of Diode-Based Chaotic Circuits: A Case Study

2020 ◽  
pp. 2150077 ◽  
Author(s):  
Léandre Kamdjeu Kengne ◽  
Jacques Kengne ◽  
Nicole Adelaïde Kengnou Telem ◽  
Justin Roger Mboupda Pone ◽  
Hervé Thierry Kamdem Tagne
Keyword(s):  
Complex Dynamics ◽  
Period Doubling ◽  
Multiple Attractors ◽  
Asymmetric Mode ◽  
Nonlinear Component ◽  
Realistic Situation ◽  
Coexistence Of Multiple Attractors ◽  
Chaotic Circuits ◽  
Route To Chaos ◽  
Antiparallel Diodes

We consider the modeling and asymmetry-induced dynamics for a class of chaotic circuits sharing the same feature of an antiparallel diodes pair as the nonlinear component. The simple autonomous jerk circuit of [J. Kengne, Z. T. Njitacke, A. N. Nguomkam, M. T. Fouodji and H. B. Fotsin, Coexistence of multiple attractors and crisis route to chaos in a novel chaotic jerk circuit, Int. J. Bifurcation Chaos Appl. Sci. Eng.26 (2016) 1650081] is used as the prototype. In contrast to current approaches where the diodes are assumed to be identical (and thus a perfect symmetric circuit), we examine the more realistic situation where the diodes have different electrical properties in spite of unavoidable scattering of parameters. In this case, the nonlinear component formed by the diodes pair displays an asymmetric current–voltage characteristic which induces asymmetry of the whole circuit. The model is described by a continuous-time 3D autonomous system (ODEs) with exponential nonlinearities. We examine the chaos mechanism with respect to system parameters both in the symmetric and asymmetric modes of operation by using bifurcation diagrams and phase space trajectory plots as the main indicators. Period doubling route to chaos, merging crisis, and multiple coexisting (i.e., two, four, or six) mutually symmetric attractors are reported in the symmetric mode of oscillation. In the asymmetric mode, several unusual nonlinear behaviors arise such as coexisting bifurcations, hysteresis, asymmetric double-band chaotic attractor, crisis, and coexisting multiple (i.e., two, three, four, or five) asymmetric attractors for some suitable ranges of parameters. Theoretical analyses and circuit experiments show a very good agreement. The results obtained in this work let us conjecture that chaotic circuits with antiparallel diodes pair are capable of much more complex dynamics than what is reported in the current literature and thus should be reconsidered accordingly in spite of the approach followed in this work.

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