Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria

Abstract

This paper studies a four-dimensional (4D) memristive system modified from the 3D chaotic system proposed by Lü and Chen. The new system keeps the symmetry and dissipativity of the original system and has an uncountable infinite number of stable and unstable equilibria. By varying the strength of the memristor, we find rich complex dynamics, such as limit cycles, torus, chaos, and hyperchaos, which can peacefully coexist with the stable equilibria. To explain such coexistence, we compute the unstable manifolds of the equilibria, find that the manifolds create a safe zone for the hyperchaotic attractor, and also find many heteroclinic orbits. To verify the existence of hyperchaos in the 4D memristive circuit, we carry out a computerassisted proof via a topological horseshoe with twodirectional expansions, as well as a circuit experiment on oscilloscope views.

An Improved Memristive Diode Bridge‐Based Band Pass Filter Chaotic Circuit

“…Due to the unique nonlinear characteristics of memristors [1], an explosive growth study of memristor based circuits has been boosted up in the past years [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Unfortunately, induced by technical handicaps in fabricating nanoscale memristor, the commercial memristor is not expected to be available in the near future.…”

“…Thus, various kinds of physically implementable equivalent circuits which can manifest the three fingerprints of memristors [17] have attracted much attention [2,[6][7][8][9][10][11][12][13][14][15][16][17][18]. Popularly, the circuits implemented by operational amplifiers and analog multipliers [7][8][9][10][11][12] as well as the circuits consisting of diode bridge cascaded with RC [13][14][15], LC [16], and RLC [18] filters have been used for experimental measurements in memristor based circuits. The most significant feature of the memristive diode bridge emulators is ungrounded limitation, which makes it as a serial expandable and flexible element in designing memristor based circuit [19].…”

A Memristor-Based Hyperchaotic Complex Lü System and Its Adaptive Complex Generalized Synchronization

“…In [19], a memristive hyperchaotic real Lü system was firstly constructed by adding a flux-controlled memristor to a traditional Lü system, which can be described by:…”

Characteristic Analysis of Fractional‐Order 4D Hyperchaotic Memristive Circuit

“…He et al concluded the characteristics of this method, such as high accuracy, fast convergence, and less computer resources consumption [40]. Recently, Li et al proposed a new 4D hyperchaotic memristive circuit [41], which possesses abundant complex dynamics. The main feature of this system is having uncountable infinite number of stable equilibria, which is significantly different from other reported chaotic systems before.…”