scholarly journals A Novel Chaotic System with Two Circles of Equilibrium Points: Multistability, Electronic Circuit and FPGA Realization

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1211 ◽  
Author(s):  
Sambas ◽  
Vaidyanathan ◽  
Tlelo-Cuautle ◽  
Zhang ◽  
Sukono ◽  
...  

This paper introduces a new chaotic system with two circles of equilibrium points. The dynamical properties of the proposed dynamical system are investigated through evaluating Lyapunov exponents, bifurcation diagram and multistability. The qualitative study shows that the new system exhibits coexisting periodic and chaotic attractors for different values of parameters. The new chaotic system is implemented in both analog and digital electronics. In the former case, we introduce the analog circuit of the proposed chaotic system with two circles of equilibrium points using amplifiers, which is simulated in MultiSIM software, version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB. In addition, we perform the digital implementation of the new chaotic system using field-programmable gate arrays (FPGA), the experimental observations of the attractors of which confirm its suitability to generate chaotic behavior.

2013 ◽  
Vol 278-280 ◽  
pp. 54-57
Author(s):  
Hong Yang

In this paper, a novel three-dimensional autonomous chaotic system with six terms and two quadratic nonlinearities is presented. Some basic dynamical properties of the new chaotic system are analyzed by means of equilibrium points, eigenvalue structures, Lyapunov exponent and Lyapunov dimension. In order to overcome the external conditions affected by the analog circuit’s chaotic system, digital implementation of the new chaotic system based on LabVIEW is also proposed. The results show that the experimental results by LabVIEW are consistent with the theoretical simulation results by Matlab, and the method is an effective digital implementation method.


2019 ◽  
Vol 29 (05) ◽  
pp. 1950067 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Abdul Jalil M. Khalaf ◽  
Zhouchao Wei ◽  
Viet-Thanh Pham ◽  
Ahmed Alsaedi ◽  
...  

This paper deals with a new modified hyperchaotic van der Pol–Duffing (MVPD) snap oscillator. Various dynamical properties of the proposed system are investigated with the help of Lyapunov exponents, stability analysis of the equilibrium points and bifurcation plots. The existence of the Hopf bifurcation is established by analyzing the corresponding characteristic equation. It is also proved that the MVPD oscillator shows multistability with coexisting attractors. Various numerical simulations are conducted and presented to show the dynamical behavior of the MVPD system. To show that the system is hardware realizable, we derive the discrete model of the MVPD system using the Euler’s method and using the hardware–software cosimulation, the proposed MVPD system is implemented in Field Programmable Gate Arrays. It is shown that the output of the digital implementations of the MVPD systems matches the numerical analysis.


2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sundarapandian Vaidyanathan ◽  
Xiong Wang

Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control.


Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
M. D. Vijayakumar ◽  
Sajjad Shaukat Jamal ◽  
Ahmed M. Ali Ali ◽  
Karthikeyan Rajagopal ◽  
Sajad Jafari ◽  
...  

Designing chaotic systems with different properties helps to increase our knowledge about real-world chaotic systems. In this article, a piecewise linear (PWL) term is employed to modify a simple chaotic system and obtain a new chaotic model. The proposed model does not have any equilibrium for different values of the control parameters. Therefore, its attractor is hidden. It is shown that the PWL term causes an offset boostable variable. This feature provides more flexibility and controllability in the designed system. Numerical analyses show that periodic and chaotic attractors coexist in some fixed values of the parameters, indicating multistability. Also, the feasibility of the system is approved by designing field programmable gate arrays (FPGA).


Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2108
Author(s):  
Mohamed Yassine Allani ◽  
Jamel Riahi ◽  
Silvano Vergura ◽  
Abdelkader Mami

The development and optimization of a hybrid system composed of photovoltaic panels, wind turbines, converters, and batteries connected to the grid, is first presented. To generate the maximum power, two maximum power point tracker controllers based on fuzzy logic are required and a battery controller is used for the regulation of the DC voltage. When the power source varies, a high-voltage supply is incorporated (high gain DC-DC converter controlled by fuzzy logic) to boost the 24 V provided by the DC bus to the inverter voltage of about 400 V and to reduce energy losses to maximize the system performance. The inverter and the LCL filter allow for the integration of this hybrid system with AC loads and the grid. Moreover, a hardware solution for the field programmable gate arrays-based implementation of the controllers is proposed. The combination of these controllers was synthesized using the Integrated Synthesis Environment Design Suite software (Version: 14.7, City: Tunis, Country: Tunisia) and was successfully implemented on Field Programmable Gate Arrays Spartan 3E. The innovative design provides a suitable architecture based on power converters and control strategies that are dedicated to the proposed hybrid system to ensure system reliability. This implementation can provide a high level of flexibility that can facilitate the upgrade of a control system by simply updating or modifying the proposed algorithm running on the field programmable gate arrays board. The simulation results, using Matlab/Simulink (Version: 2016b, City: Tunis, Country: Tunisia, verify the efficiency of the proposed solution when the environmental conditions change. This study focused on the development and optimization of an electrical system control strategy to manage the produced energy and to coordinate the performance of the hybrid energy system. The paper proposes a combined photovoltaic and wind energy system, supported by a battery acting as an energy storage system. In addition, a bi-directional converter charges/discharges the battery, while a high-voltage gain converter connects them to the DC bus. The use of a battery is useful to compensate for the mismatch between the power demanded by the load and the power generated by the hybrid energy systems. The proposed field programmable gate arrays (FPGA)-based controllers ensure a fast time response by making control executable in real time.


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