Invertible logic is a powerful new unconventional computing paradigm, providing bidirectional operations between inputs and outputs. It has found applications in important critical problems, such as integer factorization and machine learning. Here we propose a network of interconnected nonlinear systems that serve as our probabilistic bits ("p-bits") to implement invertible logic in the presence of a noise floor. In the forward (or directed) mode, the inputs are fixed in our network, yielding outputs in accordance with AND, OR, NAND, and NOR logic functions. In the reverse (inverted) mode the output is clamped in the network, and the input nodes fluctuate among all possible logical input values consistent with the different logic functions. So the system acts as a unique invertible logic circuit by exploiting the probabilistic transitions between the dynamical states of the coupled noisy nonlinear systems. Interestingly, both the directed and the inverted mode are most robust and reliable in an optimal band of moderate noise, reminiscent of stochastic resonance. The concept is verified in proof-of-principle electronic circuit experiments, demon-strating the robustness of the architecture and the potential of this idea to be realized in a wide range of physical situations.

We demonstrate the direct implementation of all basic logical operations utilizing a single bistable system driven by nonlinearly transformed input signals, in the presence of noise. Exploiting the hopping between the dynamical states of the bistable system, assisted by the noise floor, in response to the transformed inputs, allows the implementation of the full set of logic operations. So this idea can form the basis of the design of a dynamical computing element that can be rapidly morphed to yield any desired logic gate by varying just a single control parameter. Further, the results are verified in electronic circuit experiments, demonstrating the robustness of the concept and the potential of this idea to be realized in wide-ranging systems.

Reservoir Computing is an emerging machine learning framework which is a versatile option for utilising physical systems for computation. In this paper, we demonstrate how a single node reservoir, made of a simple electronic circuit, can be employed for computation and explore the available options to improve the computational capability of the physical reservoirs. We build a reservoir computing system using a memristive chaotic oscillator as the reservoir. We choose two of the available hyperparameters to find the optimal working regime for the reservoir, resulting in two reservoir versions. We compare the performance of both the reservoirs in a set of three non-temporal tasks: approximating two non-chaotic polynomials and a chaotic trajectory of the Lorenz time series. We also demonstrate how the dynamics of the physical system plays a direct role in the reservoir's hyperparameters and hence in the reservoir's prediction ability.

A two-state system driven by two inputs has been found to consistently produce a response mirroring a logic function of the two inputs, in an optimal window of moderate noise. This phenomenon is called logical stochastic resonance (LSR). We extend the conventional LSR paradigm to implement higher-level logic architecture or typical digital electronic structures via carefully crafted coupling schemes. Further, we examine the intriguing possibility of obtaining reliable logic outputs from a noise-free bistable system, subject only to periodic forcing, and show that this system also yields a phenomenon analogous to LSR, termed Logical Vibrational Resonance (LVR), in an appropriate window of frequency and amplitude of the periodic forcing. Lastly, this approach is extended to realize morphable logic gates through the Logical Coherence Resonance (LCR) in excitable systems under the influence of noise. The results are verified with suitable circuit experiments, demonstrating the robustness of the LSR, LVR and LCR phenomena. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

We first review ideas of harnessing chaotic attractors to implement robust and flexible logic gates, and recast these concepts in the context of tipping points. The central idea is as follows: The presence of tipping points in complex systems endows it with the capability to switch between very different attractors under small changes in parameter, and this feature can be exploited to obtain reliable logic operations. The binary logic outputs can be efficiently mapped to dynamical attractors bounded in different phase space regions, and the logic inputs can be simply encoded through small changes in a parameter. We then go on to extend our central idea with new implementations of multiple-input logic operations. We show explicitly that the system jumps consistently in response to an external stream of multiple inputs, thus offering robust realizations of more complex multi-input logic gates. We demonstrate that the existence of tipping points offers the advantage that very low-amplitude inputs can yield highly amplified outputs. We also show that noise may play a constructive role, enhancing the reliability of the emergent multi-input logic operations, thus strengthening the concept of generalized Logical Stochastic Resonance. These results indicate that the tipping mechanism can serve to construct general purpose computing devices, which have the added capacity to reconfigure logic functionalities efficiently by small parameter changes.

The l-glutamic acid thin films prepared using a lucrative process simplified spray pyrolysis (or) perfume atomizer technique. The absorption coefficient, refractive index, extinction coefficient, imaginary and real parts of dielectric constant, electrical and optical conductivity, optical polarization, electrical and optical susceptibility were inspected with spectrum of UV–Visible spectroscopy. The optical properties for varying molar concentration and wavelength were investigated to reveal the characteristic features of the chosen sample. In addition, the nonlinear optical constants, third-order susceptibility, nonlinear refractive index, nonlinear absorption coefficient, intensity dependent refractive coefficient and change in refractive index were also examined with Z-scan technique. The optical nonlinearities were also assayed using the Eclipse and f-scan experiments. The difference in the nonlinear optical responses relating to selected functional parameters has been considered significantly along with optical limiting behavior.

We explore the behaviour of coupled bistable systems subject to noise from two independent uncorrelated noise sources, over a range of coupling and noise strengths. We find that the interplay of coupling and noise leads to the emergence of four behavioural regimes: no synchrony and no hopping; unsynchronized hopping; synchronized hopping; synchrony without hopping. We show the occurrence of this phenomenon in a variety of bistable systems including the synthetic genetic network model, in the presence of both uniform and Gaussian noise, indicating the generality of this phenomenon. Further, we experimentally verify the different regimes of behaviour in coupled bistable electronic circuits, thus establishing its robustness.

The nonlinear optical properties of 2-Nitroaniline, which is known to be a superior nonlinear optical material, have been investigated. The optical properties, such as absorption coefficients, are analyzed with UV visible spectroscopy analyses. The third-order nonlinear optical properties of the sample are analyzed with Z-scan, Eclipse Z-scan and f-scan techniques. The nonlinear absorption coefficient, nonlinear refractive index and third-order susceptibility are examined using open aperture and closed aperture Z-scan methods. The nanoscale sensitive variations in the nonlinear optical properties are observed with the Eclipse Z-scan method. The third-order optical nonlinearities occurring in the nanoscale range are also analyzed using the f-scan method and compared with the results obtained from the Z-scan measurement. The optical limiting characteristics of the sample have also been examined for its low-power optical limiting applications.

The Guanidine carbonate thin films were deposited with a cost-effective method, namely simplified spray pyrolysis (or) perfume atomizer technique. The analyzes of nonlinear optical properties of thin films were carried out using the Z-scan and Eclipse Z-scan experiments. The linear optical properties such as linear refractive index, linear extinction coefficient, linear absorption coefficient, real part and imaginary part of dielectric constant, optical conductivity, electrical conductivity, optical susceptibility, electrical susceptibility and optical polarization were also examined using the UV–vis-NIR spectral analyses. The linear optical properties as a function of wavelength and as function of molar concentration are discussed. The nonlinear optical properties such as nonlinear absorption coefficient, nonlinear refractive index, third order susceptibility, change in refractive index and intensity dependent refractive coefficient are determined for the guanidine carbonate thin films using the Z-scan and eclipse Z-scan technique. The variation of the linear and nonlinear optical properties with respect to the chosen functional parameter has been presented. The laser damage threshold for the thin films were studied by the Q-switched Nd-YAG Laser. In addition, the investigation of optical limiting behavior also been carried out.

We identified the plausibility of the existence of strange nonchaotic attractors (SNAs) in a model of two sinusoidal driven LCR dissipative oscillators sharing a common piecewise nonlinearity. The detected strange nonchaos has been assayed through numerical studies encompassing phase space analysis, Poincaré cross sections, Lyapunov exponents, etc., The strange nonchaotic nature of attractors was examined by recurrence quantification measure. Phase synchronization features of the attractors in the SNA regime have also been included. Experimental evidences have been furnished by means of a real-time electronic circuit to reinforce the observed results. It is expected that the outcomes of the present study could facilitate the understanding and the observation of SNAs in nonlinearly coupled networks, including small-world, scale-free networks and neuronal networks.

In this paper, we report the dynamical transitions to strange non-chaotic attractors in a quasiperiodically forced state controlled-cellular neural network (SC-CNN)-based MLC circuit via two different mechanisms, namely the Heagy–Hammel route and the gradual fractalisation route. These transitions were observed through numerical simulations and hardware experiments and confirmed using statistical tools, such as maximal Lyapunov exponent spectrum and its variance and singular continuous spectral analysis. We find that there is a remarkable agreement of the results from both numerical simulations as well as from hardware experiments.

This paper presents the performance analysis of compound chaotic sequence (CCS)-based noise reduction differential chaos shift keying (NR-DCSK) system under multipath Rayleigh fading channel conditions. The special characteristics of chaotic sequences are their deterministic randomness behaviour that adds security and multipath immunity to the data when used as a carrier in communication systems. In this paper, the chaotic sequences are generated by combining the outputs of chaotic maps, such as logistic map, Chebyshev map, Bernoulli shift map, tent map, etc., leading to new complex sequences known as CCSs. This sequence possesses more randomness, overcomes severe interference levels encountered during transmission and provides higher multipath immunity compared with those of pseudo-noise (PN) codes. Since NR-DCSK is a spread spectrum technique, its performance in wireless multipath fading channels has important considerations. The CCS is used as a carrier in NR-DCSK systems, which leads to improved bit error rate (BER) performance. Comparisons of simulation results to theoretical BER expressions of additive white Gaussian noise (AWGN) and Rayleigh fading channels have been carried out to test the efficiency of the proposed CCS-based NR-DCSK system.

The energy-sharing collision of bright optical solitons in the Manakov system, governing pulse propagation in high birefringent fiber, is employed theoretically to realize optical logic gates. In particular, we successfully construct (theoretically) the universal NOR gate and the OR gate from the energy-sharing collisions of just four bright solitons which can be well described by the exact bright four-soliton solution of the Manakov system. This construction procedure has important merits such as realizing the two input gates with a minimal number of soliton collisions and possibilities of multistate logic. The recent experiments on Manakov solitons suggest the possibility of implementation of this theoretical construction of such gates and ultimately an all-optical computer.

In this work we will demonstrate the following result: when we have two coupled bistable sub-systems, each driven separately by an external logic input signal, the coupled system yields outputs that can be mapped to specific logic gate operations in a robust manner, in an optimal window of noise. So, though the individual systems receive only one logic input each, due to the interplay of coupling, nonlinearity and noise, they cooperatively respond to give a logic output that is a function of both inputs. Thus the emergent collective response of the system, due to the inherent coupling, in the presence of a noise floor, maps consistently to that of logic outputs of the two inputs, a phenomenon we term coupling induced Logical Stochastic Resonance. Lastly, we demonstrate our idea in proof of principle circuit experiments.

Certain nonlinear systems can switch between dynamical attractors occupying different regions of phase space, under variation of parameters or initial states. In this work we exploit this feature to obtain reliable logic operations. With logic output 0/1 mapped to dynamical attractors bounded in distinct regions of phase space, and logic inputs encoded by a very small bias parameter, we explicitly demonstrate that the system hops consistently in response to an external input stream, operating effectively as a reliable logic gate. This system offers the advantage that very low-amplitude inputs yield highly amplified outputs. Additionally, different dynamical variables in the system yield complementary logic operations in parallel. Further, we show that in certain parameter regions noise aids the reliability of logic operations, and is actually necessary for obtaining consistent outputs. This leads us to a generalization of the concept of Logical Stochastic Resonance to attractors more complex than fixed point states, such as periodic or chaotic attractors. Lastly, the results are verified in electronic circuit experiments, demonstrating the robustness of the phenomena. So we have combined the research directions of Chaos Computing and Logical Stochastic Resonance here, and this approach has potential to be realized in wide-ranging systems.

We construct single input logic gates using the energy sharing collisions of a minimal number of (three) bright optical solitons associated with the three soliton solution of the integrable Manakov system. As computation requires state changes to represent binary logic, here we make use of the state change of a particular soliton during its sequential collision with other two solitons for constructing single input gates. As a consequence, we clearly demonstrate the construction of various one-input logic gates such as COPY gate, NOT gate and ONE gate using energy sharing three soliton collision of Manakov system. This type of realization of logic gates just from a three soliton collision (pair-wise interaction) is clearly distinct from the earlier studies which require separate collisions of four solitons.

We propose a simple and new unified method to achieve lag, complete and anticipatory synchronizations in coupled nonlinear systems. It can be considered as an alternative to the subsystem and intentional parameter mismatch methods. This novel method is illustrated in a unidirectionally coupled RC phase shift network based Chua’s circuit. Employing feedback coupling, different types of chaos synchronization are observed experimentally and numerically in coupled identical chaotic oscillators without using time delay. With a simple switch in the experimental set up we observe different kinds of synchronization. We also analyze the coupled system with numerical simulations.