Finite-time stabilization of a perturbed chaotic finance model

Fixed-time sliding-mode distributed consensus and formation control of disturbed fractional-order multi-agent systems

In this paper, fixed-time consensus and formation control for fractional-order multi-agent systems with a dynamic virtual leader in the presence of external disturbances is investigated. Consensus is achieved in fixed-time, i.e., with a finite settling time whose upper bound is independent of the initial conditions of the agents' states. A new distributed sliding-mode control with neighborhood-based error variable is proposed to track a virtual leader in order to achieve a desired consensus in the presence of disturbances. Furthermore, the fractional Lyapunov stability theorem has been employed to prove the fixed-time stability and to estimate the upper bound of convergence. The formation of agents has also been investigated for the agents of fractional-order. Finally, several numerical simulations are provided to determine the effectiveness of the design method.

Global Existence and Fixed-Time Synchronization of a Hyperchaotic Financial System Governed by Semi-Linear Parabolic Partial Differential Equations Equipped with the Homogeneous Neumann Boundary Condition

Chaotic nonlinear dynamical systems, in which the generated time series exhibit high entropy values, have been extensively used and play essential roles in tracking accurately the complex fluctuations of the real-world financial markets. We are concerned with a system of semi-linear parabolic partial differential equations supplemented by the homogeneous Neumann boundary condition, which governs a financial system comprising the labor force, the stock, the money, and the production sub-blocks distributed in a certain line segment or planar region. The system derived by removing the terms involved with partial derivatives with respect to space variables from our concerned system was demonstrated to be hyperchaotic. We firstly prove, via Galerkin's method and establishing a priori inequalities, that the initial-boundary value problem for the concerned partial differential equations is globally well posed in Hadamard's sense. Secondly, we design controls for the response system to our concerned financial system, prove under some additional conditions that our concerned system and its controlled response system achieve drive-response fixed-time synchronization, and provide an estimate on the settling time. Several modified energy functionals (i.e., Lyapunov functionals) are constructed to demonstrate the global well-posedness and the fixed-time synchronizability. Finally, we perform several numerical simulations to validate our synchronization theoretical results.

An Image Encryption Scheme Synchronizing Optimized Chaotic Systems Implemented on Raspberry Pis

Guaranteeing security in information exchange is a challenge in public networks, such as in the highly popular application layer Message Queue Telemetry Transport (MQTT) protocol. On the one hand, chaos generators have shown their usefulness in masking data that can be recovered while having the appropriate binary string. Privacy can then be accomplished by implementing synchronization techniques to connect the transmitter and receiver, among millions of users, to encrypt and decrypt data having the correct public key. On the other hand, chaotic binary sequences can be generated on Rapsberry Pis that can be connected over MQTT. To provide privacy and security, the transmitter and receiver (among millions of devices) can be synchronized to have the same chaotic public key to encrypt and decrypt data. In this manner, this paper shows the implementation of optimized chaos generators on Raspberry Pis that are wirelessly connected via MQTT for the IoT protocol. The publisher encrypts data that are public to millions of interconnected devices, but the data are decrypted by the subscribers having the correct chaotic binary sequence. The image encryption system is tested by performing NIST, TestU01, NPCR, UACI and other statistical analyses.