Bridge the Gap Between the Lorenz System and the Chen System

Abstract

This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.

Single state feedback stabilization of unified chaotic systems and circuit implementation

“…Based on the Lorenz system, Lü system and Chen system, the uni ed chaotic system was proposed by Lü [49]. The uni ed chaotic system is described by…”

“…In this paper, we also focus on the circuit design and implementation of the uni ed chaotic system [49] so that di erent attractors can be obtained with simple adjusting. This new circuit is based on the design in [48,50].…”

Chaotic Control of Lü System via Three Methods

“…The unified chaotic system [15] is described as , system (1) belongs to Chen chaotic system [17]; when 0.8 γ = , system (1) belongs to Lü chaotic system [18]. Obviously, Lü system is a bridge between Lorenz system and Chen system, so the study of Lü system is very significant.…”

Photosynthesis rate, salinity induced grazing rate and gestation delay as determinants of the dynamics of a realistic food chain model: a stochastic approach

“…It often represents gestation time (Jana 2014;Jana et al 2014), incubation period, transport delay or can simply lump complicated biological process together, accounting only for the time requires for these process to occur. Delay parameter emphasizes on Hopf-bifurcation (Ruan 2009;Jana 2014;Jana et al 2014Jana et al , 2015 and also it causes some complex dynamical behaviors, such as double Hopf bifurcation, quasi-periodic solutions and chaos (Lü 2002;Ma et al 2008;Matouk 2008;Ding and Jiang 2011;Wang et al 2014;Ding et al 2013;Song and Xu 2013). Along with different studies of environmental stochasticity and biological delays in prey-predator system, influence of noise on a delayed system is very significant for advance study of biological system.…”