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The dynamic behavior of first-order autonomous space invariant cellular neural networks (CNNs) is investigated. It is shown that complex dynamics may occur in very simple CNN structures, described by two-dimensional templates that present only vertical and horizontal couplings. The bifurcation processes are analyzed through the computation of the limit cycle Floquet's multipliers, the evaluation of the Lyapunov exponents and of the signal spectra. As a main result a detailed and accurate two-dimensional bifurcation diagram is reported. The diagram allows one to distinguish several regions in the parameter space of a single CNN. They correspond to stable, periodic, quasi-periodic, and chaotic behavior, respectively. In particular it is shown that chaotic regions can be reached through two different routes: period doubling and torus breakdown. We remark that most practical CNN implementations exploit first order cells and space-invariant templates: so far only a few examples of complex dynamics and no complete bifurcation analysis have been presented for such networks.

The bifurcation phenomena occurring in a current mode controlled buck converter when it shifts from continuous conduction mode (CCM) to discontinuous conduction mode (DCM) have been reported. A sampled data model has been developed considering CCM as well as DCM. The bifurcation phenomena observed in such converters have been verified experimentally.

An RF phase-quadrature oscillator is analyzed. The designer "ensured" the phase-quadrature working condition through a suitable cross-coupled electrical connection between the two parts composing the complete oscillator. Through a detailed analysis of the dynamics of this oscillator, we show that device mismatch can lead to an unexpected stable working mode where the oscillator does not operate in a phase-quadrature condition. The proposed analysis has been first performed on a simplified model of the oscillator to allow the use of software packages for numerical continuation. The results of the analysis of the simplified oscillator dynamics have been then checked by means of accurate device models from a 65 nm RF technology library.

In this paper, subharmonic and chaotic behavior in current controlled DC drive has been investigated. The effects of variation of some chosen parameters on the qualitative behavior of the system have been studied. To avoid occurrence of chaos we present a method for controlling chaos applicable to DC drives. The results of numerical investigation are presented.

A new chaotic circuit is practically realized, for the first time, using a Lambert W-function. The circuit consists of three main parts. The first part employs a well-known Wilson current mirror, whereas the second part is a simple resistor at the two connected emitters of the current mirror. Both parts form a new circuit for a Lambert W-function by enabling a term of an emitter current to be simultaneously appeared on both sides of an exponential equation. Such a nonlinear equation is particularly well suited for realization of a Lambert W-function. The third part exploits a capacitor–inductor–capacitor (CLC) network and a resistor, which are connected to the nonlinear circuit of the Lambert W-function to allow for chaotic oscillations. The new circuit is capable of both a Lambert W-function and a current-tunable chaotic oscillator.

Due to their structure and complexity, chaotic systems have been introduced in several domains such as electronic circuits, commerce domain, encryption and network security. In this paper, we propose a novel multidimensional chaotic system with multiple parameters and nonlinear terms. Then, a two-phase algorithm is presented for investigating the chaotic behavior using bifurcation and Lyapunov exponent (LE) theories. Finally, we illustrate the performances of our proposal by constructing three (03) chaotic maps (3-D, 4-D and 5-D) and implementing the 3-D map on Field-Programmable-Gate-Array (FPGA) boards to generate random keys for securing a client–server communication purpose. Based on the achieved results, the proposed scheme is considered an ideal candidate for numerous resource-constrained devices and internet of the things (IoT) applications.

Following the experimental realization of memristors, researchers have focused on memristor-based circuits. Chaotic circuits can be implemented easily using a memristor due to its nonvolatile and nonlinear behavior. This study presents a memristor-based four-dimensional (4D) chaotic oscillator with a line equilibria. A memristor having quadratic memductance was utilized to implement the proposed chaotic oscillator. The 4D chaotic oscillator with quartic nonlinearity was designed as a result of the quadratic memductance. In terms of communication security, random number generation and image and audio encryption, systems with quartic nonlinearity or that are higher-dimensional are better than systems that are lower-dimensional or possess quadratic/cubic nonlinearity. The performance of the proposed chaotic circuit was investigated according to properties such as phase portraits, Jacobian matrices, equilibrium points, Lyapunov exponents and bifurcation analyses. Furthermore, the proposed system is multistable and its solutions tend to appear as twin attractors when initial conditions approach their equilibria. The Lyapunov-based nonlinear controller was constructed for controlling the proposed system having a line equilibria. The effect of the initial conditions on the controlling indicators was also studied. In conclusion, by using discrete circuit elements, the proposed circuit was constructed, and its experimental results demonstrated a good agreement with the simulation results.

In this work, a new cubic-like smooth nonlinearity is generated by modifying Chua’s piecewise-linear segmental nonlinear function using logarithmic cos-hyperbolic function implementation. A logarithmic cos-hyperbolic function possessing smooth symmetric nonlinear characteristics is implemented through CMOS-based circuit design using the current mode approach. The nonlinear design is then incorporated in a new third-order chaotic oscillator configuration to produce chaotic oscillations. This chaotic circuit is tuned to develop different attractors through the bifurcation parameter. Moreover, the dynamics of chaos such as antimonotonicity and coexistence of attractors are also depicted in circuit simulation by tuning various controlling parameters. Additionally, some numerical analyses are performed on this dynamic system to justify the existence of chaoticity and attractors’ development. This design has been optimized for low-voltage and moderately high dominant frequency of oscillations. Simulations are done using 180-nm CMOS technology in Cadence Virtuoso. Experimental results are presented to verify the workability of the proposed chaotic system.