This paper proposes new pathological element-based active device models which can be used in analysis tasks of linear(ized) analog circuits. Nullators and norators along with the Voltage Mirror-Current Mirror (VM-CM) pair (collectively known as pathological elements) are used to model the behavior of active devices in voltage-, current-and mixed-mode, also considering parasitic elements. Since analog circuits are transformed to nullor-based equivalent circuits or VM-CM pairs or as a combination of both, standard nodal analysis can be used to formulate the admittance matrix. We present a formulation method in order to build the Nodal Admittance (NA) matrix of nullor-equivalent circuits, where the order of the matrix is given by the number of nodes minus the number of nullors. Since pathological elements are used to model the behavior of active devices, we introduce a more efficient formulation method in order to compute small-signal characteristics of pathological element-based equivalent circuits, where the order of the NA matrix is given by the number of nodes minus the number of pathological elements. Examples are discussed in order to illustrate the potential of the proposed pathological elementbased active device models and the new formulation method in performing symbolic analysis of analog circuits. The improved formulation method is compared with traditional formulation methods, showing that the NA matrix is more compact and the generation of non-zero coefficients is reduced. As a consequence, the proposed formulation method is the most efficient one reported so far, since the CPU-time and memory consumption is reduced when recursive determinant-expansion techniques are used to solve the NA matrix.

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A new 3-D chaotic dynamical system with a peanut-shaped closed curve of equilibrium points is introduced in this work. Since the new chaotic system has infinite number of rest points, the new chaotic model exhibits hidden attractors. A detailed dynamic analysis of the new chaotic model using bifurcation diagrams and entropy analysis is described. The new nonlinear plant shows multi-stability and coexisting convergent attractors. A circuit model using MultiSim of the new 3-D chaotic model is designed for engineering applications. The new multi-stable chaotic system is simulated on a field-programmable gate array (FPGA) by applying two numerical methods, showing results in good agreement with numerical simulations. Consequently, we utilize the properties of our chaotic system in designing a new cipher colour image mechanism. Experimental results demonstrate the efficiency of the presented encryption mechanism, whose outcomes suggest promising applications for our chaotic system in various cryptographic applications.

SUMMARYNew nullor-based models are introduced to describe the behavior of the first generation current conveyor (CCI), second generation current conveyor (CCII), third generation current conveyor (CCIII), their inverting equivalents (ICCI(II)(III)), and/or their multiple output topologies (MO(I)CCI(II)(III)). These nullor equivalents include only grounded resistors to improve the formulation of equations in symbolic nodal analysis. In this manner, it is highlighted the usefulness of the proposed models to calculate analytical expressions in MO(I)CCI(II)(III)-based analog circuits.

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