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Transitions to Chaos and Chaos Synchronization for Solitons in the Presence of Spatially Inhomogeneous Forces

100%
Fronczak P., Hołyst J.
Acta Physica Polonica A
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2002
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vol. 101
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issue 4
465-476
EN
Motion of kink solitons in the φ^4 model in the presence of external spatially inhomogeneous forces is studied. Depending on the system parameters various routes to chaos, i.e. Feigenbaum's scenario, type-I intermittency, and chaos-chaos intermittency are observed. Synchronization of chaotic solitons is investigated.
2
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A Simulation Research on Chaotic Behavior of Parabolic and Elliptic Underwater Acoustic Ray Equations

100%
Li S., Li X.
Acta Physica Polonica A
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2013
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vol. 123
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issue 1
53-57
EN
The chaotic behavior of underwater ray system is studied. Because the parabolic equation is an approximation under small ray angle with respect to horizontal, the elliptic equation system is considered here besides the parabolic system. We pay main attention to the interval of large ray angle. A comparison between these two forms of system is performed. We find that when the ray angle is not large (θ_0=0° - 18°), the two systems show the same qualitative behavior. However, in interval of large ray angle (θ_0 ≥ 19°), if the perturbation strength is not very small, e.g. δ=0.05, the parabolic system shows regular motion, while the elliptic system exhibits chaotic behavior in most of this interval except a few quasiperiodic islands studded in the chaotic ocean. Dynamical behaviors of the two systems show surprising difference.
3
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Fast Chaos with Slow p-n Junction Diodes

80%
Mykolaitis G., Tamaševičiūtė E., Miškinis R., Bumelienė S., Tamaševičius A.
Acta Physica Polonica A
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2008
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vol. 113
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issue 3
971-974
EN
We demonstrate both experimentally and numerically that slow recovery p -n junction diodes can be exploited to generate chaos at high megahertz frequencies. An extremely simple resonator consisting of an inductor in parallel with a diode when externally periodically driven exhibits chaotic response.
4
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Characteristics of Complexity in Selected Economic Models in the Light of Nonlinear Dynamics

80%
Jakimowicz A.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
542-546
EN
The catastrophe theory and deterministic chaos constitute the basic elements of economic complexity. Elementary catastrophes were the first remarkable form of nonlinear, topological complexity that were thoroughly studied in economics. Another type of catastrophe is the complexity catastrophe, namely an increase in the complexity of a system beyond a certain threshold which marks the beginning of a decrease in a system's adaptive capacity. As far as the ability to survive is concerned, complex adaptive systems should function within the range of optimal complexity which is neither too low or too high. Deterministic chaos and other types of complexity follow from the catastrophe theory. In general, chaos is seemingly random behavior of a deterministic system which stems from its high sensitivity to the initial condition. The theory of nonlinear dynamical systems, which unites various manifestations of complexity into one integrated system, runs contrary to the assumption that markets and economies spontaneously strive for a state of equilibrium. The opposite applies: their complexity seems to grow due to the influence of classical economic laws.
5
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Criticality Characteristics of Current Oil Price Dynamics

80%
Drożdż S., Kwapień J., Oświęcimka P.
Acta Physica Polonica A
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2008
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vol. 114
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issue 4
699-702
EN
Methodology that recently leads us to predict to an amazing accuracy the date (July 11, 2008) of reverse of the oil price up trend is briefly summarized and some further aspects of the related oil price dynamics elaborated. This methodology is based on the concept of discrete scale invariance whose finance-prediction-oriented variant involves such elements as log-periodic self-similarity, the universal preferred scaling factor λ≈2, and allows a phenomenon of the "super-bubble". From this perspective the present (as of August 22, 2008) violent - but still log-periodically decelerating - decrease of the oil prices is associated with the decay of such a "super-bubble" that has started developing about one year ago on top of the longer-term oil price increasing phase (normal bubble) whose ultimate termination is evaluated to occur in around mid 2010.
6
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Application of Ultrafast Schottky Diodes to High Megahertz Chaotic Oscillators

80%
Mykolaitis G., Tamaševičius A., Bumelienė S., Namajūnas A., Pyragas K., Pyragas V.
Acta Physica Polonica A
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2005
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vol. 107
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issue 2
365-368
EN
The considered chaotic oscillator consists of an amplifier, 2nd order LC resonator, Schottky diode and an extra capacitor in parallel to the diode. The diode plays the role of a nonlinear device. Chaotic oscillations are demonstrated numerically and experimentally at low as well as at high megahertz frequencies, up to 250 MHz.
7
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Controlling Chaos in Damped and Driven Morse Oscillator via Slave-Master Feedback

80%
Behnia S., Akhshani A., Panahi M., Asadi R.
Acta Physica Polonica A
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2013
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vol. 123
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issue 1
7-12
EN
The dynamical behavior of the Morse oscillator is investigated primarily by means of the Lyapunov exponent and bifurcation diagrams. Then, the problem of controlling chaos for this oscillator is studied using a new method introduced by Behnia and Akhshani, which is based on the construction of slave-master feedback. In the control model based on slave-master feedback, the oscillator as the slave system is coupled with a dynamical system as the master, so its implementation becomes quite simple and similar statements can be made for the high dimensional cases. The validity of this method is verified by numerical simulations. The obtained results show the effectiveness of the proposed control model.
8
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B-Spline Solution and the Chaotic Dynamics of Troesch's Problem

80%
Caglar H., Caglar N., Ozer M.
Acta Physica Polonica A
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2014
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vol. 125
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issue 2
554-560
EN
A B-spline method is presented for solving the Troesch problem. The numerical approximations to the solution are calculated and then their behavior is studied and commenced. The chaotic dynamics exhibited by the solutions of Troesch's problem as they were derived by the decomposition method approximation are examined and an approximate critical value for the parameter λ is introduced also in this study. For the parameter value slightly less than λ ≈ 2.2, the solutions begin to show successive bifurcations, finally entering chaotic regimes at higher λ values. The effectiveness and accuracy of the B-spline method is verified for different values of the parameter, below its critical value, where the first bifurcation occurs.
9
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Route to Chaos in Generalized Logistic Map

80%
Rak R., Rak E.
Acta Physica Polonica A
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2015
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vol. 127
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issue 3A
A-113-A-117
EN
We postulate a generalization of well-known logistic map to open the possibility of optimization the modelling process of the population evolution. For proposed generalized equation we illustrate the character of the transition from regularity to chaos for the whole spectrum of model parameters. As an example we consider specific cases for both periodic and chaotic regime. We focus on the character of the corresponding bifurcation sequence and on the quantitative nature of the resulting attractor as well as its universal attribute (Feigenbaum constant).
10
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Current Log-Periodic View on Future World Market Development

80%
Drożdż S., Kwapień J., Oświęcimka P., Speth J.
Acta Physica Polonica A
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2008
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vol. 114
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issue 3
539-546
EN
Applicability of the concept of financial log-periodicity is discussed and encouragingly verified for various phases of the world stock markets development in the period 2000-2010. In particular, a speculative forecasting scenario designed in the end of 2004, that properly predicted the world stock market increases in 2007, is updated by setting some more precise constraints on the time of duration of the present long-term equity market bullish phase. A termination of this phase is evaluated to occur in around November 2009. In particular, on the way towards this dead-line, a Spring-Summer 2008 increase is expected. On the precious metals market a forthcoming critical time signal is detected at the turn of March/April 2008 which marks a tendency for at least a serious correction to begin.
11
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Random Unitary Matrices Associated to a Graph

70%
Kondratiuk P., Życzkowski K.
Acta Physica Polonica A
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2013
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vol. 124
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issue 6
1098-1105
EN
We analyze composed quantum systems consisting of k subsystems, each described by states in the n-}dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual subsystems and edges denoting a generic interaction, modeled by random unitary matrices of order n^2. The global evolution operator is represented by a unitary matrix of size N = n^{k}. We investigate statistical properties of such matrices and show that they display spectral properties characteristic to the Haar random unitary matrices provided the corresponding graph is connected. Thus basing on random unitary matrices of a small size n^2 one can construct a fair approximation of large random unitary matrices of size n^{k}. Graph-structured random unitary matrices investigated here allow one to define the corresponding structured ensembles of random pure states.
12
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Local Stable or Unstable Regions in 2-Dimensional Chaotic Forms: Examples and Simulations

61%
Skiadas C.
Acta Physica Polonica A
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2013
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vol. 124
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issue 6
1082-1086
EN
We analyze 2-}dimensional chaotic forms resulting from very simple systems based on two chaotic characteristics that is rotation and parallel movement or translation in geometric terms. Reflection is another alternative, along with rotation, for several interesting chaotic formations. Rotation and translation are very common types of movements in the world around us. Chaotic or non-chaotic forms arise from these two main generators. The rotation-translation chaotic case presented is based on the theory we analyzed in the book and in the paper. An overview of the chaotic flows in rotation-translation is given. There is observed the presence of chaos when discrete rotation-translation equation forms are introduced. In such cases the continuous equations analogue of the discrete cases is useful. Characteristic cases and illustrations of chaotic attractors and forms are analyzed and simulated. The analysis of chaotic forms and attractors of the models presented is given along with an exploration of the characteristic or equilibrium points. Applications in the fields of astronomy-astrophysics (galaxies), chaotic advection (the sink problem) and Von Karman streets are presented.
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