Finite-time synchronization of tunnel-diode-based chaotic oscillators

Abstract

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel-diode-based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulations followed by PSPICE experiment are presented to show the feasibility of the proposed method.

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

“…These graphs show that the numerical finite-time of synchronization is t q rN U = 0.2 μs, which respects the finite-time condition t rN U ≤ t rT H [47]. Figure 5c gives the time evolution of the adaptive feedback controller u(t) which exponentially decreases towards a stable state just before the numerical finite-time synchronization t rN U is reached.…”

“…In the present paper, based on the Lyapunov function a fractional adaptive finite-time synchronization reflecting the method in [47] is proposed for fractional-order versions of the circuit in [43]. Then, a new key system for encryption on digital cryptography is found, using the proposed finite-time synchronization scheme which is more secure and more powerful than an existing key system of integerorder synchronization [22].…”

Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design

“…According to J. C. Sprott, the part of the controller in brown box (Fig. 6), simulates the absolute value function; the sign function is simulated by the part in the orange box, of the same figure (Sprott 2000;Louodop et al 2014). With the help of the Kirchhoff law, and taking into account that the operational amplifiers are ideal devices, the states of the whole network satisfy the set of nonlinear differential equations: 2.…”

“…Due to its diverse applications, synchronization phenomenon in complex network has attracted great attentions (Motter et al 2006;Restrepo et al 2006;Arenas et al 2006;Chen and Zhou 2006;Bowong andKakmeni 2004, 2003;Fotsin and Daafouz 2005;Louodop et al 2013;Tchitnga et al 2013;Louodop et al 2014;Megam et al 2014b, a). Controlled synchronization, with the aim of imposing a desired behavior to a member of a network and then inferring the same behavior in the whole network, represents a recent problem in complex networks (CornejoPerez et al 2012).…”

Coherent motion of chaotic attractors

“…We found that the phenomenon is not system specific restricted to these jerk systems only, but generic. We investigated other examples [23][24][25][26], the paradigmatic Rössler system, a coupled tunnel diode model, and a Josephson junction-based jerk model. In all of them, we observed coherent motion, but the exchange of leadership appears only for the Josephson junction-based jerk model, apart from the one described in this manuscript (details can be seen in the Appendices A, B, and C).…”