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Number of results: 10
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Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation

Marco Reit Michael Berens Wolfgang Mathis
Archives of Electrical Engineering | 2016 | vol. 65 | No 2 June | 337-347 | DOI: 10.1515/aee-2016-0025
Keywords Andronov-Hopf bifurcation nonlinear amplifier ambiguities
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Abstract

Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.

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Authors and Affiliations

Marco Reit
Michael Berens
Wolfgang Mathis

Divergent bifurcations of stationary motion modes of wheeled vehicle model with controlled wheel module

Alexandr Kravchenko Vladimir Verbitskii Valery Khrebet Natalia Velmagina Andrey Muranov
Teka Commission of Motorization and Power Industry in Agriculture | 2016 | vol. 16 | No 3
Keywords wheel module stability adhesion coefficient slipping forces divergent bifurcation
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Abstract

An alternative approach of the determining of conditions of safe stability loss of rectilinear motion of a wheeled vehicle model with controlled wheel module in the sense of N.N. Bautin is considered. The slipping forces are presented accurate within cubic expansion terms in the skid angles. Terms and conditions of safe stability loss depend on the ratio between the coefficients of resistance to the skid, the adhesion coefficients in the transverse direction of the axes and the parameter of torsional stiffness of the controlled wheel module. The presented approach to the analysis of real bifurcations related to the divergent loss of rectilinear motion mode stability has a clear geometric pattern: if in the vicinity of rectilinear motion at subcritical speed, there are additionally two unstable circular stationary states, then the stability limit is of dangerous nature in the sense of N.N. Bautin; if two circular stationary modes exist at supercritical speed, the limit of the stability loss in the parameter space of the longitudinal velocity is safe in the sense of N.N. Bautin. Analysis of the number of stationary modes in the vicinity of the critical velocity of rectilinear motion is performed for the obtained determining equation - cubic binomial.
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Authors and Affiliations

Alexandr Kravchenko
Vladimir Verbitskii
Valery Khrebet
Natalia Velmagina
Andrey Muranov

New Construction Methods and Performance Analysis of WINDMI Chaotic System

Thair A. Salih
International Journal of Electronics and Telecommunications | 2022 | vol. 68 | No 1 | 129-136 | DOI: 10.24425/ijet.2022.139860
Keywords chaotic signal FPAA bifurcation psd correlation
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Abstract

Chaos is an active topic of study in the field of secure communication systems that have garnered much consideration in recent years because of excessive sensitivity to a simple change in its initial conditions. In this paper, the essential features of the suggested WINDMI chaotic system like the phase portraits of the attractors, bifurcation, PSD, correlation, and balance property of the windmi chaotic system have been depicted in detail through MATLAB tools simulations and circuital application. The bifurcation examination detects a wealthy and attractive characteristic of the proposed windmi chaotic oscillator such as periodical multiple bifurcations, has two stable states chaotic demeanor, periodical windows, and recapture bifurcations. In this paper, after exploring the dynamic features of the windmi chaos paradigm, a practical chaotic circuit is implemented on the fpaa chip. Eventually, the circuit practical results of the windmi chaotic attractors present similarities with numerical simulations. The importance of the work is reflected in the use of field programmable analog array in the implementation of the windmi oscillator, and the possibility of varying the initial condition during the operation of the system. An unlimited number of signals can be generated, which enables it to be used as an oscillator utilized in many transceiver systems, that utilized an unlimited number of signals.
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Authors and Affiliations

Thair A. Salih
1
  1. Northern Technical University, Iraq

Determination of Hopf bifurcation sets of a chemical reactors by two-parameter continuation method

Marek Berezowski
Chemical and Process Engineering | 2020 | vol. 41 | No 3 | 221-227 | DOI: 10.24425/cpe.2020.132544
Keywords chemical reactor Hopf bifurcation thank reactor bifurcation diagram steady states stability dynamics
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Abstract

A two-parameter continuation method was developed and shown in the form of an example, allowing determination of Hopf bifurcation sets in a chemical reactor model. Exemplary calculations were made for the continuous stirred tank reactor model (CSTR). The set of HB points limiting the range of oscillation in the reactor was determined. The results were confirmed on the bifurcation diagram of steady states and on time charts. The method is universal and can be used for various models of chemical reactors.

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Authors and Affiliations

Marek Berezowski

Controlling bifurcations in high-speed rotors utilizing active gas foil bearings

Anastasios Papadopoulos Ioannis Gavalas Athanasios Chasalevris
Bulletin of the Polish Academy of Sciences Technical Sciences | 2023 | 71 | 6 | e146796 | DOI: 10.24425/bpasts.2023.146796
Keywords bifurcation control Hopf bifurcation active gas foil bearings high speed rotors nonlinear control
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Abstract

High-speed rotors on gas foil bearings (GFBs) are applications of increasing interest due to their potential to increase the power-toweight ratio in machines and also formulate oil-free design solutions. The gas lubrication principles render lower (compared to oil) power loss and increase the threshold speed of instability in rotating systems. However, self-excited oscillations may still occur at circumferential speeds similar to those in oil-lubricated journal bearings. These oscillations are usually triggered through Hopf bifurcation of a fixed-point equilibrium (balanced rotor) or secondary Hopf bifurcation of periodic limit cycles (unbalanced rotor). In this work, an active gas foil bearing (AGFB) is presented as a novel configuration including several piezoelectric actuators that shape the foil through feedback control. A finite element model for the thin foil mounted in some piezoelectric actuators (PZTs), is developed. Second, the gas-structure interaction is modelled through the Reynolds equation for compressible flow. A simple physical model of a rotating system consisting of a rigid rotor and two identical gas foil bearings is then defined, and the dynamic system is composed with its unique source of nonlinearity to be the impedance forces from the gas to the rotor and the foil. The third milestone includes a linear feedback control scheme to stabilize (pole placement) the dynamic system, linearized around a speed-dependent equilibrium (balanced rotor). Further to that, linear feedback control is applied in the dynamic system utilizing polynomial feedback functions in order to overcome the problem of instability.
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Authors and Affiliations

Anastasios Papadopoulos
1
Ioannis Gavalas
1
ORCID: ORCID
Athanasios Chasalevris
1
ORCID: ORCID
  1. National Technical University of Athens, Athens, Greece

A new multistable jerk chaotic system, its bifurcation analysis, backstepping control-based synchronization design and circuit simulation

Sundarapandian Vaidyanathan Khaled Benkouider Aceng Sambas
Archives of Control Sciences | 2022 | vol. 32 | No 1 | 123-152 | DOI: 10.24425/acs.2022.140868
Keywords chaos jerk systems bifurcation multistability attractors backstepping control and circuit design
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Abstract

In this work, we present results for a new dissipative jerk chaotic system with three quadratic terms in its dynamics.We describe the bifurcation analysis for the new jerk system and also show that the proposed system exhibits multi-stability. Next, we describe a backstepping control-based synchronization design for a pair of new jerk chaotic systems. MATLAB simulations are put forth to exhibit the various findings in this work. Furthermore, we exhibit a circuit simulation for the new jerk system using MultiSim.
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Authors and Affiliations

Sundarapandian Vaidyanathan
1
Khaled Benkouider
2
Aceng Sambas
3
  1. School of Electrical and Computing, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600092, Tamil Nadu, India
  2. Non Destructive Testing Laboratory, Automatic Department, Jijel University, BP 98, 18000, Jijel, Algeria
  3. Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya 46196, West Java, Indonesia

Non-bifurcation behavior of laminated composite plates under in-plane compression

Mehdi Bohlooly Fotovat Tomasz Kubiak
Bulletin of the Polish Academy of Sciences Technical Sciences | 2024 | 72 | 2 | e148874 | DOI: 10.24425/bpasts.2024.148874
Keywords non-bifurcation equilibrium path laminates antisymmetric extension-bending
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Abstract

The paper deals with bifurcation and/or non-bifurcation post-buckling curves of composite plates under biaxial compression. For different lay-up sequences, a coupling, i.e. extension-bending (EB) is considered. The current investigations present distinct equilibrium paths describing when they have bifurcation-type and/or non-bifurcation-type responses. The novel parameter (i.e. EB coupling imperfection) is calculated to show the amount of non-bifurcation in the equilibrium path as a quantitative parameter. For the case of non-square plates, a novel mixed-mode analysis is conducted. The effects of different characters in laminated composites such as layer arrangement, loading ratio, aspect ratio, and boundary conditions are investigated. A novel result concluded in the numerical examples where there are some possibilities to have different mode shapes in linear and non-linear buckling analysis. FEM results of ANSYS software verify the results of analytical equations.
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Authors and Affiliations

Mehdi Bohlooly Fotovat
1
ORCID: ORCID
Tomasz Kubiak
1
ORCID: ORCID
  1. Department of Strength of Materials, Lodz University of Technology, Stefanowskiego 1/15, 90-537 Lodz, Poland

A new two-scroll 4-D hyperchaotic system with a unique saddle point equilibrium, its bifurcation analysis, circuit design and a control application to complete synchronization

Sundarapandian Vaidyanathan Irene M. Moroz Aceng Sambas
Archives of Control Sciences | 2023 | vol. 33 | No 2 | 277-298 | DOI: 10.24425/acs.2023.146276
Keywords hyperchaos hyperchaotic systems bifurcation analysis multi-stability analysis synchronization Multisim circuit simulation
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Abstract

In this work, we present new results for a two-scroll 4-D hyperchaotic system with a unique saddle point equilibrium at the origin. The bifurcation and multi-stability analysis for the new hyperchaotic system are discussed in detail. As a control application, we develop a feedback control based on integral sliding mode control (ISMC) for the complete synchronization of a pair of two-scroll hyperchaotic systems developed in this work. Numerical simulations using Matlab are provided to illustrate the hyperchaotic phase portraits, bifurcation diagrams and synchronization results. Finally, as an electronic application, we simulate the new hyperchaotic system using Multisim for real-world implementations.
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Authors and Affiliations

Sundarapandian Vaidyanathan
1
Irene M. Moroz
2
Aceng Sambas
3 4
  1. Centre for Control Systems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600092, Tamil Nadu, India
  2. Mathematical Institute, University of Oxford, Andrew Wiles Building, ROQ, Oxford Ox2 6GG, UK
  3. Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Gong Badak, 21300, Terengganu, Malaysia
  4. Department of Mechanical Engineering, Universitas MuhammadiyahTasikmalaya, Tasikmalaya 46196,West Java, Indonesia

A new modified WINDMI jerk system with exponential and sinusoidal nonlinearities, its bifurcation analysis, multistability, circuit simulation and synchronization design

Mohamad Afendee Mohamed Sundarapandian Vaidyanathan Fareh Hannachi Aceng Sambas P. Darwin
Archives of Control Sciences | 2023 | vol. 33 | No 4 | 711-735 | DOI: 10.24425/acs.2023.148878
Keywords chaos jerk systems chaotic systems Lyapunov exponents bifurcation multistability circuit simulation backstepping control
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Abstract

In this work, a new 3-D modified WINDMI chaotic jerk system with exponential and sinusoidal nonlinearities is presented and its dynamical behaviours and properties are investigated. Firstly, some properties of the system are studied such as equilibrium points and their stability, Lyapunov exponents and Kaplan-Yorke dimension. Also, we study the new jerk system dynamics using numerical simulations and analyses, including phase portraits, Lyapunouv exponent spectrum, bifurcation diagram and Poincaré map, 0-1 test. Next, we exhibit that the new 3-D chaotic modified WINDMI jerk system has multistability with coexisting chaotic attractors. Moreover, we design an electronic circuit using MultiSim 14.1 for real implementation of the modified WINDMI chaotic jerk system. Finally, we design an active synchronization scheme for the complete synchronization of the modified WINDMI chaotic jerk systems via backstepping control.
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Authors and Affiliations

Mohamad Afendee Mohamed
1
Sundarapandian Vaidyanathan
2 3
Fareh Hannachi
4
Aceng Sambas
1
P. Darwin
5
  1. Faculty of Information and Computing,Universiti Sultan Zainal Abidin, Terengganu, Malaysia
  2. Centre for ControlSystems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600062 Tamil Nadu, India
  3. Faculty of Information and Computing, Universiti Sultan Zainal Abidin Terengganu, Malaysia
  4. Larbi Tebessi University – Tebessi routede constantine, 12022, Tebessa, Algeria
  5. Department of Computer Science and EngineeringRajalakshmi Institute of Technology, Kuthambakkam, Chennai-600 124, Tamil Nadu, India

Comparison of main geometric characteristics of deformed sphere and standard spheroid

Vasyl Kovalchuk Ivaïlo M. Mladenov
Bulletin of the Polish Academy of Sciences Technical Sciences | 2023 | 71 | 5 | e147058 | DOI: 10.24425/bpasts.2023.147058
Keywords deformed sphere standard spheroid sphericity index tipping (bifurcation) point for geodesics elliptic integrals and functions
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Abstract

In the paper we compare the geometric descriptions of the deformed sphere (i.e., the so-called λ-sphere) and the standard spheroid (namely, World Geodetic System 1984’s reference ellipsoid of revolution). Among the main geometric characteristics of those two surfaces of revolution embedded into the three-dimensional Euclidean space we consider the semi-major (equatorial) and semi-minor (polar) axes, quartermeridian length, surface area, volume, sphericity index, and tipping (bifurcation) point for geodesics. Next, the RMS (Root Mean Square) error is defined as the square-rooted arithmetic mean of the squared relative errors for the individual pairs of the discussed six main geometric characteristics. As a result of the process of minimization of the RMS error, we have obtained the proposition of the optimized value of the deformation parameter of the λ-sphere, for which we have calculated the absolute and relative errors for the individual pairs of the discussed main geometric characteristics of λ-sphere and standard spheroid (the relative errors are of the order of 10−6 – 10−9). Among others, it turns out that the value of the,sup> flattening factor of the spheroid is quite a good approximation for the corresponding value of the deformation parameter of the λ-sphere (the relative error is of the order of 10−4).
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Authors and Affiliations

Vasyl Kovalchuk
1
ORCID: ORCID
Ivaïlo M. Mladenov
2 3
ORCID: ORCID
  1. Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland
  2. Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
  3. Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria

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