We have used a system of globally coupled double-well Duffing oscillators under an enhanced resonance condition to design and implement Dual Input Multiple Output (DIMO) logic gates. In order to enhance the resonance, the first oscillator in the globally coupled system alone is excited by two forces out of which one acts as a driving force and the other will be either sub-harmonic or super-harmonic in nature. We report that for an appropriate coupling strength, the second force coherently drives and enhances not only the amplitude of the weak first force to all the coupled systems but also drives and propagates the digital signals if any given to the first system. We then numerically confirm the propagation of any digital signal or square wave without any attenuation under an enhanced resonance condition for an amplitude greater than a threshold value. Further, we extend this idea for computing various logical operations and succeed in designing theoretically DIMO logic gates such as AND/NAND, OR/NOR gates with globally coupled systems.
We report the propagation of a square wave signal in a quasi-periodically driven Murali-Lakshmanan-Chua (QPDMLC) circuit system. It is observed that signal propagation is possible only above a certain threshold strength of the square wave or digital signal and all the values above the threshold amplitude are termed as 'region of signal propagation'. Then, we extend this region of signal propagation to perform various logical operations like AND/NAND/OR/NOR and hence it is also designated as the 'region of logical operation'. Based on this region, we propose implementing the dynamic logic gates, namely AND/NAND/OR/NOR, which can be decided by the asymmetrical input square waves without altering the system parameters. Further, we show that a single QPDMLC system will produce simultaneously two outputs which are complementary to each other. As a result, a single QPDMLC system yields either AND as well as NAND or OR as well as NOR gates simultaneously. Then we combine the corresponding two QPDMLC systems in a cross-coupled way and report that its dynamics mimics that of fundamental R-S flip-flop circuit. All these phenomena have been explained with analytical solutions of the circuit equations characterizing the system and finally the results are compared with the corresponding numerical and experimental analysis. Nonlinear dynamics based computing is an emerging field which can replace silicon chips and is becoming increasingly popular in nonlinear and chaotic dynamics, and computing research. Actually, Boolean based silicon chips are extremely logical in their operations. These logical operations can be classified into two groups, namely combinational logic circuits and sequential logic circuits. The basic building blocks for combinational logic circuits are the logic gates, namely AND, OR, NOT, NAND, NOR, etc., whereas the basic building block for sequential logic circuits is the flip-flop. Here, we have proposed a new mechanism by using a quasi-periodically driven nonlinear dynamical system exhibiting a strange non-chaotic attractor for constructing the logic gates AND/NAND/OR/NOR and fundamental R-S flip-flop circuit with Murali-LakshmananChua circuit as an example. By only imposing constraints on the logic high and logic low values of the input signal, we are able to implement these dynamic logic gates and flip-flop. In fact, without altering the system parameters, we point out how the logical operations can be decided by the asymmetrical input square waves. Consequently, dynamic computing using the behaviour of nona) Electronic mail: venkatesh.sprv@gmail.com b) Electronic mail: av.phys@gmail.com c) Electronic mail: lakshman@cnld.bdu.ac.in linear dynamical systems is shown to be quite implementable in hardware devices. Our results also show that nonlinearity is more significant than the existence of chaos for design of the logic gates and latches.
Additional sinusoidal and different non-sinusoidal periodic perturbations applied to the periodically forced nonlinear oscillators decide the maintainance or inhibitance of chaos. It is observed that the weak amplitude of the sinusoidal force without phase is sufficient to inhibit chaos rather than the other non-sinusoidal forces and sinusoidal force with phase. Apart from sinusoidal force without phase, i.e., from various non-sinusoidal forces and sinusoidal force with phase, square force seems to be an effective weak perturbation to suppress chaos. The effectiveness of weak perturbation for suppressing chaos is understood with the total power average of the external forces applied to the system. In any chaotic system, the total power average of the external forces is constant and is different for different nonlinear systems. This total power average decides the nature of the force to suppress chaos in the sense of weak perturbation. This has been a universal phenomenon for all the chaotic non-autonomous systems. The results are confirmed by Melnikov method and numerical analysis. With the help of the total power average technique, one can say whether the chaos in that nonlinear system is to be supppressed or not.
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