Hopf bifurcation, antimonotonicity and amplitude controls in the chaotic Toda jerk oscillator: analysis, circuit realization and combination synchronization in its fractional-order form

In this paper, an autonomous Toda jerk oscillator is proposed and analysed. The autonomous Toda jerk oscillator is obtained by converting an autonomous two-dimensional Toda oscillator with an exponential nonlinear term to a jerk oscillator. The existence of Hopf bifurcation is established during the stability analysis of the unique equilibrium point. For a suitable choice of the parameters, the proposed autonomous Toda jerk oscillator can generate antimonotonicity, periodic oscillations, chaotic oscillations and bubbles. By introducing two additional parameters in the proposed autonomous Toda jerk oscillator, it is possible to control partially or totally the amplitude of its signals. In addition, electronic circuit realization of the proposed Toda jerk oscillator is carried out to confirm results found during numerical simulations. The commensurate fractional-order version of the proposed autonomous chaotic Toda jerk oscillator is studied using the stability theorem of fractional-order oscillators and numerical simulations. It is found that periodic oscillations and chaos exist in the fractional-order form of the proposed Toda jerk oscillator with order less than three. Finally, combination synchronization of two fractional-order proposed autonomous chaotic Toda jerk oscillators with another fractional-order proposed autonomous chaotic Toda jerk oscillator is analysed using the nonlinear feedback control method

Antimonotonicity, Crisis and Multiple Attractors in a Simple Memristive Circuit

Peer reviewedPostprin

A locally active discrete memristor model and its application in a hyperchaotic map

© 2022 Springer Nature Switzerland AG. Part of Springer Nature. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1007/s11071-021-07132-5The continuous memristor is a popular topic of research in recent years, however, there is rare discussion about the discrete memristor model, especially the locally active discrete memristor model. This paper proposes a locally active discrete memristor model for the first time and proves the three fingerprints characteristics of this model according to the definition of generalized memristor. A novel hyperchaotic map is constructed by coupling the discrete memristor with a two-dimensional generalized square map. The dynamical behaviors are analyzed with attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and dynamic behavior distribution diagram. Numerical simulation analysis shows that there is significant improvement in the hyperchaotic area, the quasi-periodic area and the chaotic complexity of the two-dimensional map when applying the locally active discrete memristor. In addition, antimonotonicity and transient chaos behaviors of system are reported. In particular, the coexisting attractors can be observed in this discrete memristive system, resulting from the different initial values of the memristor. Results of theoretical analysis are well verified with hardware experimental measurements. This paper lays a great foundation for future analysis and engineering application of the discrete memristor and relevant the study of other hyperchaotic maps.Peer reviewedFinal Accepted Versio

Multistable dynamics and control of a new 4D memristive chaotic Sprott B system

This work proposes and investigates the dynamic behavior of a new memristive chaotic Sprott B system. One of the interesting features of this system is that it has a bias term that can adjust the symmetry of the proposed model, inducing both homogeneous and heterogeneous behaviors. Indeed, the introduced memristive system can turn from rotational symmetry (RS) to rotational symmetry broken (RSB) system in the presence or the absence of this bias term. In the RS system (i.e., absence of the bias term), pairs of symmetric attractors are formed, and the scenario of attractor merging is observed. Coexisting symmetric attractors and bifurcations with up to four solutions are perfectly investigated. In the RSB system (i.e., the bias term is non-zero), many interesting phenomena are demonstrated, including asymmetric attractors, coexisting asymmetric bifurcations, various types of coexisting asymmetric solutions, and period-doubling transition to chaos. We perfectly demonstrate that the new asymmetric/symmetric memristive system exhibits the exciting phenomenon of partial amplitude control (PAC) and offset boosting. Also, we show how it is possible to control the amplitude and the offset of the chaotic signals generated for some technological exploitation. Finally, coexisting solutions (i.e., multistability) found in the novel memristive system are further controlled based on a linear augmentation (LA) scheme. Our numerical findings demonstrated the effectiveness of the control technic through interior crisis, reverse period-doubling scenario, and symmetry restoring crisis. The coupled memristive system remains stable with its unique survived periodic attractor for higher values of the coupling strength

Low-Cost Inventions and Patents

Inventions have led to the technological advances of mankind. There are inventions of all kinds, some of which have lasted hundreds of years or even longer. Low-cost technologies are expected to be easy to build, have little or no energy consumption, and be easy to maintain and operate. The use of sustainable technologies is essential in order to move towards a greater global coverage of technology, and therefore to improve human quality of life. Low-cost products always respond to a specific need, even if no in-depth analysis of the situation or possible solutions has been carried out. It is a consensus in all industrialized countries that patents have a decisive influence on the organization of the economy, as they are a key element in promoting technological innovation. Patents must aim to promote the technological development of countries, starting from their industrial situations

ANALYSIS AND STUDY OF RESPONSE SIGNALS, FROM A FOURTH ORDER NON LINEAR ELECTRICCIRCUIT, UNDER THE INFLUENCE OF AN EXTERNAL STIMULATION

ΣΤΗΝ ΔΙΑΤΡΙΒΗ ΑΥΤΗ ΜΕΛΕΤΗΣΑΜΕ ΤΗ ΔΥΝΑΜΙΚΗ ΕΝΟΣ ΑΥΤΟΝΟΜΟΥ ΚΑΙ ΜΗ ΑΥΤΟΝΟΜΟΥ ΤΕΤΑΡΤΗΣ ΤΑΞΗΣ ΗΛΕΚΤΡΙΚΟΥ ΚΥΚΛΩΜΑΤΟΣ ΒΑΣΙΣΜΕΝΟΥ ΣΤΟ ΓΕΝΙΚΕΥΜΕΝΟ ΚΥΚΛΩΜΑ CHUA ΤΡΙΤΗΣ ΤΑΞΗΣ. ΓΙΑ ΤΟ ΜΗ ΑΥΤΟΝΟΜΟ ΚΥΚΛΩΜΑ, ΚΛΕΙΔΩΜΑΤΑ ΦΑΣΗΣ, ΗΜΙΠΕΡΙΟΔΙΚΟΤΗΤΑ ΔΥΟ &ΤΡΙΩΝ ΣΥΧΝΟΤΗΤΩΝ ΠΑΡΑ ΤΗΡΟΥΝΤΑΙ ΚΑΘΩΣ ΟΙ ΧΑΟΤΙΚΟΙ ΕΛΚΥΣΤΕΣ ΔΗΜΙΟΥΡΓΟΥΝΤΑΙ ΜΕ ΕΣΩΤΕΡΙΚΗ ΚΡΙΣΗ. ΓΙΑ ΤΙΣ ΕΠΙΛΕΓΜΕΝΕΣ ΤΙΜΕΣ ΠΑΡΑΜΕΤΡΩΝ ΤΟ ΧΩΡΙΣ ΔΙΕΓΕΡΣΗ ΣΥΣΤΗΜΑ ΕΙΝΑΙ ΕΝΑΣ ΤΑΛΑΝΤΩΤΗΣ. ~ΤΑΝ ΤΟ ΚΥΚΛΩΜΑ ΟΔΗΓΕΙΤΑΙ ΑΠΟ ΠΗΓΗ ΗΜΙΤΟΝΙΚΗΣ ΤΑΣΗΣ, ΟΙ ΚΑΤΑΣΤΑΣΕΙΣ ΚΛΕΙΔΩΜΑΤΟΣ ΦΑΣΗΣ ΔΗΜΙΟΥΡΓΟΥΝ ΜΙΑ ΚΑΤΑΣΚΕΥΗ ΓΝΩΣΤΗ ΩΣ ΣΚΑΛΑ ΤΟΥ ΔΙΑΒΟΛΟΥ. Η ΧΑΟΤΙΚΗ ΣΥΜΠΕΡΙΦΟΡΑ ΤΟΥ ΣΥΣΤΗΜΑΤΟΣ ΕΞΑΡΤΑΤΑΙ ΙΣΧΥΡΑ ΑΠΟ ΤΗΜΗ ΓΡΑΜΜΙΚΟΤΗΤΑ ΤΟΥ ΜΗ ΓΡΑΜΜΙΚΟΥ ΑΝΤΙΣΤΑΤΗ. ΣΤΗΝ ΠΕΡΙΠΤΩΣΗ ΤΟΥ ΑΥΤΟΝΟΜΟΥ ΚΥΚΛΩΜΑΤΟΣ ΠΑΡΑΤΗΡΟΥΜΕ ΤΟΝ ΔΡΟΜΟ ΠΡΟΣ ΤΟ ΧΑΟΣ ΜΕ ΔΙΠΛΑΣΙΑΣΜΟ ΠΕΡΙΟΔΟΥ, ΚΑΘΩΣ Κ ΑΙ ΑΝΤΙΜΟΝΟΤΟΝΙΚΟΤΗΤΑ, ΜΙΑ ΑΝΑΣΤΡΟΦΗ ΑΚΟΛΟΥΘΙΑ ΔΙΠΛΑΣΙΑΣΜΟΥ ΤΑΣΗΣ ΠΟΥ ΣΥΜΦΩΝΕΙΙ ΜΕ ΤΗ ΘΕΩΡΗΤΙΚΗ ΑΝΑΛΥΣΗ ΤΩΝ BIER ΚΑΙ BOUNTIS. ΣΤΗ ΧΑΟΤΙΚΗ ΠΕΡΙΟΧΗ ΠΑΡΑΤΗΡΕΙΤΑΙ ΔΙΑΛΕΙΠΤΟΤΗΤΑ ΕΠΑΓΟΜΕΝΗ ΑΠΟ ΚΡΙΣΗ. Ο ΕΛΕΓΧΟΣ ΤΗΣ ΧΑΟΤΙΚΗΣ ΣΥΜΠΕΡΙΦΟΡΑΣ ΜΕ ΕΞΩΤΕΡΙΚΗ ΗΜΙΤΟΝΙΚΗ ΠΗΓ Η ΑΠΟΚΑΛΥΠΤΕΙ ΟΤΙ ΥΠΑΡΧΕΙ ΜΙΑ ΕΛΑΧΙΣΤΗ ΤΙΜΗ ΠΛΑΤΟΥΣ ΠΟΥ ΟΔΗΓΕΙ ΤΟ ΚΥΚΛΩΜΑ ΣΕ ΕΥΣΤΑΘΗ ΚΑΤΑΣΤΑΣΗ ΠΕΡΙΟΔΟΥ-1. ΜΕΛΕΤΗΣΑΜΕ ΕΠΙΣΗΣ ΤΟΝ ΕΛΕΓΧΟ ΤΗΣ ΧΑΟΤΙΚΗΣ ΣΥΜΠΕΡΙΦΟΡΑΣ ΜΕ "ΑΠΟΡΡΟΦΗΤΗ ΤΑΛΑΝΤΩΣΕΩΝ", ΕΝΑ ΓΡΑΜΜΙΚΟ ΠΑΡΑΛΛΗΛΟ RLC ΚΥΚΛΩΜΑ.IN THIS THESIS WE STUDY THE DYNAMICS OF AUTONOMOUS AND NON AUTONOMOUS FOURTH ORDER ELECTRIC CIRCUITS BASED ON THE THIRD ORDER CANONICAL REALIZATION OF CHUA'S CIRCUIT. IN THE CASE OF THE NONAUTONMOUS CIRCUIT, PHASE LOCKED STATES, TWO-FREQUENCY AND THREE-FRE QUENCY QUASIPERIODICITY ARE OBSERVED WHILE CHAOTIC ATTRACTORS ARE CREATED BY INTERIOR CRISIS. FOR THE PARAMETER VALUES WE HAVE CHOSEN, THE UNFORCED CIRCUIT IS AN OSCILLATOR. WHEN THE CIRCUIT IS DRIVEN BY ASINUSOIDAL VOLTAGE SOURCE, THE PHASE LOCKED STATES CREATE A SET KNOWN AS DEVIL'S STAIRCASE. THE CHAOTIC BEHAVIOR OF THE CIRCUIT IS STRONGLY DEPEND ON THE NONLINEARITY OF THE NONLINEAR RESISTOR. IN THE CASE OF THE AUTONOMOUS CIRCUIT WE OBSERVE THE PERIOD-DOUBLING ROUTE TO CHAOS, AS WELL AS ANTIMONOTONICITY, A REVERSE PERIOD-DOUBLING SEQUENCE. ANTIMONOTONICITY IS APPEARED ACCORDING TO THE THEORITICAL PREDICTIONS OF BIER AND BOUNTIS. IN THE CHAOTIC REGIME CRISIS INDUCED INTERMITTENCY IS OBSERVED. THE CONTROL OF CHAOTIC BEHAVIOR USING AN EXTERNAL SINISOIDAL SIG NAL REVEALS, THAT THERE IS A MINIMUM VALUE OF THE AMPLITUDE, WHICH LEADS THE CIRCUIT TO A PERIOD-1 STEADY STATE. WE HAVE ALSOSTUDIED THE CONTROL OF CHAOTIC BEHAVIOR USING AN 'ABSORBER', A LINEAR PARALLEL RLC CIRCUIT