Santo Banerjee

Synchronization between variable time-delayed systems and cryptography

In this letter we consider the phenomena of chaos synchronization for time-delayed dynamical systems when the delay is not constant. As an example we have considered the autonomous continuous-time-delayed system studied by Ucar, when the delay is modulated. The region in the parameter space for the onset of chaos is explored and both analytical and numerical methodologies are used for the analysis of the synchronization of two such systems, using the Krasovskii-Lyapunov functional. We have applied the adaptive coupling method for synchronization and studied the implementation of cryptography for this coupled system. The message extraction procedure is illustrated with the help of simulated results.

Global optimization of an optical chaotic system by Chaotic Multi Swarm Particle Swarm Optimization

The control and estimation of unknown parameters of chaotic systems are a daunting task till date from the perspective of nonlinear science. Inspired from ecological co-habitation, we propose a variant of Particle Swarm Optimization (PSO), known as Chaotic Multi Swarm Particle Swarm Optimization (CMS-PSO), by modifying the generic PSO with the help of the chaotic sequence for multi-dimension unknown parameter estimation and optimization by forming multiple cooperating swarms. This achieves load balancing by delegating the global optimizing task to concurrently operating swarms. We apply it successfully in estimating the unknown parameters of an autonomous chaotic laser system derived from Maxwell-Bloch equations. Numerical results and comparison demonstrate that for the given system parameters, CMS-PSO can identify the optimized parameters effectively evolving at each iteration to attain the pareto optimal solution with small population size and enhanced convergence speedup.

Turing instabilities and spatio-temporal chaos in ratio-dependent Holling–Tanner model

In this paper we consider a modified spatiotemporal ecological system originating from the temporal Holling-Tanner model, by incorporating diffusion terms. The original ODE system is studied for the stability of coexisting homogeneous steady-states. The modified PDE system is investigated in detail with both numerical and analytical approaches. Both the Turing and non-Turing patterns are examined for some fixed parametric values and some interesting results have been obtained for the prey and predator populations. Numerical simulation shows that either prey or predator population do not converge to any stationary state at any future time when parameter values are taken in the Turing-Hopf domain. Prey and predator populations exhibit spatiotemporal chaos resulting from temporal oscillation of both the population and spatial instability. With help of numerical simulations we have shown that Turing-Hopf bifurcation leads to onset of spatio-temporal chaos when predators diffusivity is much higher compared to prey population. Our investigation reveals the fact that Hopf-bifurcation is essential for the onset of spatiotemporal chaos.

Synchronization of spatiotemporal semiconductor lasers and its application in color image encryption

Optical chaos is a topic of current research characterized by high-dimensional nonlinearity which is attributed to the delay-induced dynamics, high bandwidth and easy modular implementation of optical feedback. In light of these facts, which add enough confusion and diffusion properties for secure communications, we explore the synchronization phenomena in spatiotemporal semiconductor laser systems. The novel system is used in a two-phase colored image encryption process. The high-dimensional chaotic attractor generated by the system produces a completely randomized chaotic time series, which is ideal in the secure encoding of messages. The scheme thus illustrated is a two-phase encryption method, which provides sufficiently high confusion and diffusion properties of chaotic cryptosystem employed with unique data sets of processed chaotic sequences. In this novel method of cryptography, the chaotic phase masks are represented as images using the chaotic sequences as the elements of the image. The scheme drastically permutes the positions of the picture elements. The next additional layer of security further alters the statistical information of the original image to a great extent along the three-color planes. The intermediate results during encryption demonstrate the infeasibility for an unauthorized user to decipher the cipher image. Exhaustive statistical tests conducted validate that the scheme is robust against noise and resistant to common attacks due to the double shield of encryption and the infinite dimensionality of the relevant system of partial differential equations.

Applications of chaos and nonlinear dynamics in engineering

Preface.- Fluctuation Relations and Chaotic Dynamics.- Monsoon Chaos and Wind Turbine System.- Fractal and its Application in Epileptic Seizure.- Chaos Synchronization: Communications and Symbolic Analysis.- Chaos Synchronization: Sytems and Circuits.

Multiplexing synchronization and its applications in cryptography

In this paper, we consider the problem of multiplexing in chaotic synchronization where the transmitter is a delayed dynamical system, and there is more than one receiver represented by the usual nonlinear systems. Sufficient condition of synchronization is derived analytically from the Krasovskii?Lyapunov functional consisting of multidimensional error vectors. These are then substantiated numerically. Later, we show how these results can be used in chaotic cryptography where the communication between the transmitter and the receiver can carry more than one message. Finally, it is demonstrated how the messages can be recovered safely.

Semi-empirical study of ortho-cresol photo degradation in manganese-doped zinc oxide nanoparticles suspensions.

The optimization processes of photo degradation are complicated and expensive when it is performed with traditional methods such as one variable at a time. In this research, the condition of ortho-cresol (o-cresol) photo degradation was optimized by using a semi empirical method. First of all, the experiments were designed with four effective factors including irradiation time, pH, photo catalyst’s amount, o-cresol concentration and photo degradation % as response by response surface methodology (RSM). The RSM used central composite design (CCD) method consists of 30 runs to obtain the actual responses. The actual responses were fitted with the second order algebraic polynomial equation to select a model (suggested model). The suggested model was validated by a few numbers of excellent statistical evidences in analysis of variance (ANOVA). The used evidences include high F-value (143.12), very low P-value (<0.0001), non-significant lack of fit, the determination coefficient (R2 = 0.99) and the adequate precision (47.067). To visualize the optimum, the validated model simulated the condition of variables and response (photo degradation %) be using a few number of three dimensional plots (3D). To confirm the model, the optimums were performed in laboratory. The results of performed experiments were quite close to the predicted values. In conclusion, the study indicated that the model is successful to simulate the optimum condition of o-cresol photo degradation under visible-light irradiation by manganese doped ZnO nanoparticles.

Can complexity decrease in congestive heart failure

The complexity of a signal can be measured by the Recurrence period density entropy (RPDE) from the reconstructed phase space. We have chosen a window based RPDE method for the classification of signals, as RPDE is an average entropic measure of the whole phase space. We have observed the changes in the complexity in cardiac signals of normal healthy person (NHP) and congestive heart failure patients (CHFP). The results show that the cardiac dynamics of a healthy subject is more complex and random compare to the same for a heart failure patient, whose dynamics is more deterministic. We have constructed a general threshold to distinguish the border line between a healthy and a congestive heart failure dynamics. The results may be useful for wide range for physiological and biomedical analysis.

Generalized variable projective synchronization of time delayed systems

We study generalized variable projective synchronization between two unified time delayed systems with constant and modulated time delays. A novel Krasovskii-Lyapunov functional is constructed and a generalized sufficient condition for synchronization is derived analytically using the Lyapunov stability theory and adaptive techniques. The proposed scheme is valid for a system of n-numbers of first order delay differential equations. Finally, a new neural oscillator is considered as a numerical example to show the effectiveness of the proposed scheme.

Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model

Simulations are performed to investigate the nonlinear dynamics of a (2+1)-dimensional chemotaxis model of Keller–Segel (KS) type, with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely used to simulate self-organization in many biological systems. We show that the corresponding dynamics may lead to steady-states, to divergencies in a finite time as well as to the formation of spatiotemporal irregular patterns. The latter, in particular, appears to be chaotic in part of the range of bounded solutions, as demonstrated by the analysis of wavelet power spectra. Steady-states are achieved with sufficiently large values of the chemotactic coefficient (χ) and/or with growth rates r below a critical value rc. For r>rc, the solutions of the differential equations of the model diverge in a finite time. We also report on the pattern formation regime, for different values of χ, r and of the diffusion coefficient D.