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Summary Over the last two decades, chaotification has received increasing attention from various communities of science and engineering. This paper aims at developing a unified chaotification framework for generating desired higher‐dimensional dissipative hyperchaotic systems by using a single‐parameter controller. The main idea is to use a block diagonal matrix in the design of the nominal system, so as to construct a desired hyperchaotic system. Specifically, the proposed scheme is to assign desired closed‐loop poles to the controlled system, allocating the corresponding numbers of eigenvalues with positive real parts at two types of saddle‐focus equilibria. For the non‐degenerate case, the number of positive Lyapunov exponents of the controlled system is given by the largest number of positive Lyapunov exponents of the desired hyperchaotic system. Two representative examples are given to illustrate and verify the proposed design method. Finally, the digital signal processor is employed to implement the above 10‐dimensional hyperchaotic systems, and the experimental observation is also given. Copyright © 2015 John Wiley & Sons, Ltd.

This paper introduces a novel approach for generating continuous-time autonomous hyperchaotic systems with multiple positive Lyapunov exponents. In detail, this paper develops two general design principles for constructing various hyperchaotic systems with desired numbers of positive Lyapunov exponents. Two typical examples are then given to verify the proposed design principle. In particular, the developed method can design hyperchaotic systems with any multiple positive Lyapunove exponents by following a unified procedure compared with the traditional trial-and-error approach.

This paper investigates n-dimensional discrete-time systems with modulus of triangular wave functions. First, a proof is given to the existence of chaos in the sense of Li–Yorke. Then, taking the three-dimensional case as a typical example, a circuit is designed under the condition of a limited region, with experimental results demonstrated.