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We formulate a mathematical model for the classical Chua’s circuit with two nonlinear resistors in terms of a system of nonlinear ordinary differential equations. The existence of two nonlinear resistors implies that the system has three equilibrium points. The behaviour of the trajectory in a neighbourhood of each equilibrium point depends on the eigenvalues of the system. The eigenvalues can be obtained from a cubic polynomial equation. It turns out that all possible solutions of the cubic equation lead to six types of equilibrium points, namely, stable node, unstable node, saddle node, stable focus node, unstable focus node, saddle focus node. The chaotic behaviour of the circuit occurs when the equilibrium point is a stable focus node or a saddle focus node. The hidden attractor of our Chua’s system is localized through a suitable initial point.

We introduce the Tracy-Singh sum for operators on a Hilbert space, generalizing both the Tracy-Singh sum for matrices and the tensor sum for operators. The Tracy-Singh sum is shown to be compatible with algebraic operations and order relations. Then we establish a binomial theorem involving Tracy-Singh sums, and its consequences. We also investigate continuity, convergence, and norm bounds for Tracy-Singh sums. Moreover, we derive operator identities involving Tracy-Singh sums and certain operator functions defined by power series.

We generalize the notions of Khatri-Rao sums for matrices and tensor sums for Hilbert space operators to KhatriRao sums for Hilbert space operators. This kind of operator sum is compatible with algebraic operations and order relations. We investigate its analytic properties, including continuity, convergence, and norm bounds. We also discuss the role of selection operator that relates Khatri-Rao sums to Tracy-Singh sums and Khatri-Rao products. Binomial theorem involving Khatri-Rao sums and its consequences are then established.