In this paper, a three-dimensional novel chaotic system and its projective synchronisation are investigated. The proposed chaotic system has no equilibria. The topological structure of proposed chaotic system is different form Lorenz, Rossler and Chen systems. Different qualitative and quantitative tools such as time series, phase plane, Poincare section, bifurcation plot, Lyapunov exponents, Lyapunov spectrum, and Lyapunov dimension are used to evidence the chaotic behaviour of the proposed system. Further, the projective synchronisation between the proposed chaotic systems is achieved using nonlinear active control. Active control laws are designed, by using sum of the relevant variables of the proposed chaotic systems, to ensure the convergence of error dynamics. The required global asymptotic stability condition is derived using Lyapunov stability theory. Simulation is done in MATLAB environment to verify the theoretical approach. Simulation results reveal that the objectives of the paper are achieved successfully.

中文翻译：

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具有Poincare映射的降落伞和拇指形状的新型无平衡混沌系统及其投影同步

本文研究了三维新型混沌系统及其投影同步。所提出的混沌系统没有平衡。拟议的混沌系统的拓扑结构不同于Lorenz，Rossler和Chen系统。时间序列，相平面，庞加莱截面，分叉图，李雅普诺夫指数，李雅普诺夫谱和李雅普诺夫维等不同的定性和定量工具被用来证明所提出系统的混沌行为。此外，使用非线性主动控制可以实现所提出的混沌系统之间的投影同步。通过使用所提出的混沌系统的相关变量之和来设计主动控制律，以确保误差动态的收敛。使用Lyapunov稳定性理论导出了所需的全局渐近稳定性条件。仿真是在MATLAB环境中完成的，以验证理论方法。仿真结果表明，本文的目标得以成功实现。