Improving chaos-based pseudo-random generators in finite-precision arithmetic

Nonlinear Dynamics - One of the widely-used ways in chaos-based cryptography to generate pseudo-random sequences is to use the least significant bits or digits of finite-precision numbers defined...     

The inverse coefficient problem of heat conduction for an isotropic body

We discuss a method for determining the complex of thermophysical characteristics of isotropic materials based on the solution of the two-dimensional nonstationary heat conduction problem for a layer subject to a narrow-band heating by a heat flow. We take account of the finite speed of thermal action of an annular heater.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 4–9.     

A novel memristive time–delay chaotic system without equilibrium points

Memristor and time–delay are potential candidates for constructing new systems with complex dynamics and special features. A novel time–delay system with a presence of memristive device is proposed in this work. It is worth noting that this memristive time–delay system can generate chaotic attractors although it possesses no equilibrium points. In addition, a circuitry implementation of such time–delay system has been introduced to show its feasibility.     

Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique

In this paper, the stabilization and synchronization of a complex hidden chaotic attractor is shown. This article begins with the dynamic analysis of a complex Lorenz chaotic system considering the vector field properties of the analyzed system in the Cn domain. Then, considering first the original domain of attraction of the complex Lorenz chaotic system in the equilibrium point, by using the required set topology of this domain of attraction, one hidden chaotic attractor is found by finding the intersection of two sets in which two of the parameters, r and b, can be varied in order to find hidden chaotic attractors. Then, a backstepping controller is derived by selecting extra state variables and establishing the required Lyapunov functionals in a recursive methodology. For the control synchronization law, a similar procedure is implemented, but this time, taking into consideration the error variable which comprise the difference of the response system and drive system, to synchronize the response system with the original drive system which is the original complex Lorenz system.     

Hyperchaotic memristive system with hidden attractors and its adaptive control scheme

In this research work a novel 4-D memristive system is presented. The proposed system belongs to the category of dynamical systems with hidden attractors as it displays a line of equilibrium points. Also, it has an hyperchaotic dynamical behavior in a particular range of its parameters space. System’s behavior is investigated through numerical simulations, by using well-known tools of nonlinear theory, such as phase portrait, bifurcation diagram, Lyapunov exponents and Poincaré map. Next, the case of chaos control of the system with unknown parameters using adaptive control method is investigated. Finally, an electronic circuit realization of the novel hyperchaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.     

Implementation and study of the nonlinear dynamics of a memristor-based Duffing oscillator

An electronic model of Duffing oscillator with a characteristic memristive nonlinear element is proposed instead of the classical cubic nonlinearity. The memristive Duffing oscillator circuit system is mathematically modeled, and the stability analysis presents the evolution of the proposed system. The dynamical behavior of this circuit is investigated through numerical simulations, statistical analysis, and real-time hardware experiments, which have been carried out under the external periodic force. The chaotic dynamics of the circuit is studied by means of phase diagram. It is found that the proposed circuit system shows complex behaviors, like bifurcations and chaos, three tori, transient chaos, and intermittency for a certain range of circuit parameters. The observed phenomena and scenario are illustrated in detail through experimental and numerical studies of memristive Duffing oscillator circuit. The existence of regular and chaotic behaviors is also verified by using 0–1 test measurements. In addition, the robustness of the signal strength is confirmed through signal-to-noise ratio. The numerically observed results are confirmed from the laboratory experiment.     

Distributed Consensus Tracking Control of Chaotic Multi-Agent Supply Chain Network: A New Fault-Tolerant,Finite-Time,and Chatter-Free Approach

Over the last years, distributed consensus tracking control has received a lot of attention due to its benefits, such as low operational costs, high resilience, flexible scalability, and so on. However, control methods that do not consider faults in actuators and control agents are impractical in most systems. There is no research in the literature investigating the consensus tracking of supply chain networks subject to disturbances and faults in control input. Motivated by this, the current research studies the fault-tolerant, finite-time, and smooth consensus tracking problems for chaotic multi-agent supply chain networks subject to disturbances, uncertainties, and faults in actuators. The chaotic attractors of a supply chain network are shown, and its corresponding multi-agent system is presented. A new control technique is then proposed, which is suitable for distributed consensus tracking of nonlinear uncertain systems. In the proposed scheme, the effects of faults in control actuators and robustness against unknown time-varying disturbances are taken into account. The proposed technique also uses a finite-time super-twisting algorithm that avoids chattering in the system’s response and control input. Lastly, the multi-agent system is considered in the presence of disturbances and actuator faults, and the proposed scheme’s excellent performance is displayed through numerical simulations.