Obviously, the problem of IFSHPS is more difficult than the problem of FSHPS. Since master system states and slave system states have been inverted with respect to the FSHPS, the new scheme has been called the inverse full-state hybrid projective synchronization (IFSHPS). Recently, an interesting scheme has been introduced, where each master system state synchronizes with a linear constant combination of slave system states. In this type of synchronization, each slave system state achieves synchronization with linear combination of master system states. It has been widely used in the synchronization of fractional chaotic (hyperchaotic) systems. Therefore, studies on synchronization of such fractional systems with different orders should be considered further.Īmong all types of chaos synchronization schemes, full-state hybrid projective synchronization (FSHPS) is one of the most noticeable types. Authors have tended to synchronize fractional systems with the same orders. In order to determine chaos synchronization between such fractional-order systems, some synchronization schemes were constructed as summarized in Table 1. investigated the fractional-order form of a three-dimensional chaotic autonomous system with only one stable equilibrium. Fractional-order forms of systems without equilibrium were reported in, while fractional-order forms of systems with an infinite number of equilibrium points were presented in. When considering the effects of fractional derivatives on systems with hidden attractors, a few fractional-order forms of systems with hidden attractors have been introduced. Authors have focused on local fractional diffusion equations in fractal heat transfer, fractal LC-electric circuit, and new rheological models. Moreover, it is worth noting that local fractional derivatives with special functions have received significant attention in different areas. In recent years, there has been an increasing interest in the stability of fractional systems. The fractional derivatives play important roles in the field of mathematical modeling of numerous models such as fractional model of regularized long-wave equation, Lienard’s equation, fractional model of convective radial fins, modified Kawahara equation, etc. ĭifferent definitions and main properties of fractional calculus have been reported in the literature. Hidden attractors have received considerable attention recently because of their roles in theoretical and practical problems. It is worth noting that systems with stable equilibria are systems with ‘hidden attractors’. In addition, the generalized Sprott C system with only two stable equilibria was introduced in. Interestingly, the six-term system with stable equilibria exhibited a double-scroll chaotic attractor. A six-term system with stable equilibria was presented in. By using the center manifold theory and normal form method, Wei investigated delayed feedback on such a chaotic system with two stable node-foci. found an unusual Lorenz-like chaotic system with two stable node-foci. In spite of the fact that the Yang-Chen system connected the original Lorenz system and the original Chen system, it was not diffeomorphic with the original Lorenz and Chen systems. Yang and Chen proposed a chaotic system with one saddle and two stable node-foci. Several attempts have been made to investigate chaotic systems with stable equilibria. However, recent evidence suggests that chaos can be observed in 3D autonomous systems with stable equilibria. It has previously been observed that common 3D autonomous chaotic systems, such as Lorenz system, Chen system, Lü system, or Yang’s system, have one saddle and two unstable saddle-foci. Many three-dimensional (3D) autonomous chaotic systems have been found and reported in the literature. Applications of chaos have been witnessed in various areas ranging from path planning generator, secure communications, audio encryption scheme, image encryption, to truly random number generator. There has been a dramatic increase in studying chaos and systems with chaotic behavior in the past decades.