Figure 2 - uploaded by S. O. Starkov
Content may be subject to copyright.
Source publication
An approach to design of chaotic oscillators with preassigned spectral characteristics is proposed and its practical realization is demonstrated. The basic idea of the approach is to form a frequency-selective circuit and to connect it to a harmonic oscillator so as to provide generation of chaotic oscillations with given spectral characteristics.
Context in source publication
Similar publications
Citations
... Some methods for designing the feedback network have been proposed in [20][21][22] that could achieve pre-assigned spectral characteristics of the chaotic oscillations. In these designs more than one (L − R)-(C 1 − C 2 ) type tanks are involved in the feedback network. ...
This manuscript presents modifications of the standard Colpitts circuit by replacing one of the capacitors in C1 − C2 potential divider by a pair of back-to-back connected diode varactor. This introduces a nonlinearity of diode varactor type in the feedback signal generation itself. The dynamic capacitance of the varactor pair varies nonlinearly with the output voltage. The proposed modification facilitates generation of enriched frequency components with enhanced power. Both C1 and C2 were alternately replaced by the diode varactor and results were compared with the standard oscillator with fixed-value capacitors. The analysis is based on basic numerical tools such as Lyapunov exponents, bifurcation diagram, phase trajectories and power spectra.
... Chaos in the Colpitts oscillator has been reported first by Kennedy [1][2][3]. Later, the chaotic behavior of this oscillator has been investigated by several authors due to its applications in encryption and modulation methods applied to communication systems [15][16][17][18][19][20][21][22]. ...
In this paper, nonlinear observer design for a chaotic system has been investigated. Indeed, a high gain observer and a sliding mode observer are proposed to the Colpitts circuit. The synthesis of these observers took place under certain sufficient conditions arising directly necessary and sufficient conditions established for nonlinear systems. Comparing with the results obtained by these observers, the high gain observer showed a good ability to reconstruct the states of the chaotic system and providing a small mean squared error compared to that of the sliding mode observer.
... In the early 2000s, researchers developed and experimentally demonstrated the feasibility to generate directly chaos in the microwave band [1][2][3][4][5]. The first Microwave Chaotic Oscillator (MCO), based on the Colpitts oscillator [6], was proposed and realized by Panas et al [1]; which generates chaotic signals in the frequency band 900-1000 MHz. ...
... The first Microwave Chaotic Oscillator (MCO), based on the Colpitts oscillator [6], was proposed and realized by Panas et al [1]; which generates chaotic signals in the frequency band 900-1000 MHz. Later, several approaches have been proposed in order to broaden the bandwidth of the microwave chaotic signals [2][3][4][5]. ...
... The first application of the DCC technology is in the UWB technology [10]. The combination of the two technologies is feasible since it is possible experimentally to generate directly RF chaotic carrier from MCO [1], [2] and [3]. Therefore, the principle idea of the UWB DCC technology is resumed to replace the chaotic source of the transmitter presented in Fig. 1 by an UWB chaotic generator. ...
A new non-coherent chaotic modulation technique based on adaptive decision threshold is proposed for the UltraWideBand
(UWB) Direct Chaotic Communication (DCC) technology. The principal advantages of the proposed
technique are: (1) Removing the threshold problem of the classical Chaotic On-Off Keying modulation technique which
uses a nonzero decision threshold; (2) Providing a high throughput comparing to the others techniques since it do not
uses any delay at the modulation; (3) Reducing the transmitted power, thanks to a transmitted bit energy devised by two.
The obtained simulation results show high Bit Error Rate performances of the proposed technique applied in an UWB
DCC system. In addition, the new chaotic modulation is more suitable in all DCC-based communications schemes.
... Chaos in the Colpitts oscillator has been reported first by Kennedy [5]. Later, the chaotic behaviour of this oscillator has been investigated by several authors [6], [7], [8]. All these studies of the chaotic Colpitts oscillator have been limited in low frequencies, in the order of tens of KHz, where the BJT is modeled as a piecewise linear circuit. ...
... The results show the occurrences of broader-collision bifurcations and moreover, border bifurcations corresponding to singularities of the Jacobian of the system. The feedback loop in a Colpitts oscillator, which provides conditions for chaotic signal generation, can be designed so that the output of the oscillator has preassigned spectral characteristics [8], [13]. ...
A detailed description and analysis on the behaviour of a bipolar junction transistor in chaotic operation is presented. Bipolar Junction Transistors (BJTs) are basic ingredients of chaotic Colpitts oscillators, which aim at generating chaotic signals for secure communications. The high frequency operation of the chaotic oscillators is a challenging issue due to the parasitic capacitance of the junctions of a BJT. The presented analysis shows that the parasitic capacitances have adverse effects on the oscillator's operation. They may generate conditions for chaotic oscillations or destroy them as well. Simulation results show that in order to determine more accurately the chaotic spectral signature and the performance of the system, the impact of the parasitic capacitances need to be taken into account during the design and analysis phase of the system.
... In particular this interest deals with certain properties of chaotic signals and systems. For example using relatively simple electronic circuits one can obtain wideband chaotic oscillations [3], and a number of different chaotic regimes can be obtained using the same chaotic source. There is a number of chaotic oscillators models developed by now, which are widely used for different laboratory purposes. ...
... This is also confirmed by direct evaluation of the spectrum discussed in previous section. So to syntheses chaotic oscillators with preassigned spectrum, it is necessary to consider oscillators of higher dimensions as in [3, 4]. A chaotic source produced of oscillations in ~0.5…3 Mhz band is described i n [3]. ...
... So to syntheses chaotic oscillators with preassigned spectrum, it is necessary to consider oscillators of higher dimensions as in [3, 4]. A chaotic source produced of oscillations in ~0.5…3 Mhz band is described i n [3]. Chaotic oscillator and frequency-selective network forming the oscillation spectrum make this chaotic source. ...
Recent investigations show that wireless communication systems are a very promising application area of chaotic dynamics. At the same time synthesis of chaotic oscillators suitable for IC implementation and producing chaotic oscillations in the specified frequency band is a problem. Here the problem of synthesis of RC chaotic oscillator with preassigned spectrum is discussed. Spectral properties of known RC chaotic oscillators are analyzed. Some conjectures regarding the structure of RC chaotic oscillator are formulated.
In this study, a voltage-controlled memristor was designed and connected in parallel with an inductor-capacitor to form an oscillator circuit. The memristor, as a natural electronic equivalent for building biological neurons, enabled this oscillator circuit to simulate the four types of firing patterns generated by neurons. By means of a two-parameter scan, a dynamic map of the discharges was created, allowing a more efficient dynamic analysis of the field, and the results were compared with the potassium-sodium ion model of the neuron. The analysis of the stability of the equilibrium point allowed a better understanding of the complex discharge mechanisms generated by the system. The results of the hardware tests and the numerical analysis were in agreement.
Absbvld-Recent investigations show that wireless communication systems are a very promising application area of chaotic dynamics. At the same time synthesis of chaotic oscillators suitable for IC implementation and producing chaotic oscillations in the specified frequency band is a problem. Here the problem of synthesis of RC chaotic oscillator with broadband spectrum is discussed. Indw tents-RC chaotic oscillators, broadband chaotic oscillation, chaos.
Aujourd'hui, les signaux chaotiques sont de plus en plus utilisés dans les systèmes de communication. Dans cet article, nous nous intéressons à la synchronisation des systèmes chaotiques à l'aide d'un observateur à modes glissants. L'article est composé de deux parties. La première concerne l'étude et la réalisation en basse fréquence ( 100kHz) d'un oscillateur chaotique de Colpitts, qui sera utilisé par la suite comme émetteur. Les différents comportements de l'oscillateur sont étudiés et les résultats expérimentaux sont présentés et commentés. Dans la deuxième partie, un observateur à modes glissants est réalisé afin de reconstruire les différents états de l'émetteur. Pour cela, nous utilisons la sortie de l'émetteur (un signal chaotique), que l'on injecte dans le récepteur (observateur à modes glissants) afin de reconstruire tous les états de l'oscillateur chaotique. Nous montrons dans ce travail, la possibilité de réaliser un observateur à modes glissants en utilisant des composants électroniques simples et standards. Ainsi nous étudions le phénomène de réticence (“chattering” en anglais) et son effet sur le fonctionnement de l'observateur.
