On the study of nonlinear dynamics of complex chemical reaction systems

Abstract

With ever-increasing attentions being paid to complex systems such as the life system, soft matter, and nano-systems, theoretical studies of non-equilibrium nonlinear problems involved in chemical dynamics are now of general interest. In this mini-review, we mainly give a brief introduction to some frontier topics in this field, namely, nonlinear state-state dynamics, nonlinear chemical dynamics on complex networks, and nonlinear dynamics in mesoscopic chemical reaction systems. Deep study of these topics will make great contribution to discovering new laws of chemical dynamics, to exploring new control methods of complex chemical processes, to figuring out the very roles of chemical processes in the life system, and to crosslinking the scientific study of chemistry, physics and biology.When driven far from equilibrium, nonlinear chemical reactions often show a variety of selforganization behavior, including chemical oscillations, waves, chaos and patterns [1] . Recently, the study of such nonlinear phenomena in 'complex' systems, such as the life system and surface systems as soft matter, has drawn growing interest. For example, oscillations of protein concentration in synthetic gene networks, calcium oscillations as well as waves in cardiac tissues, reaction rate oscillations, spiral waves, and spatiotemporal chaos in surface catalytic reactions, have been observed [2][3][4][5][6][7] . It was demonstrated that such 'nonlinear chemistry phenomena (NCP)' play rather important roles in regulating the functioning processes in real systems, including gene expression, signal propagating, neuronal processing, catalytic reactivity as well as selectivity, and so on. Therefore, it is of great importance to study how the NCPs are formed in complex chemical systems, how they transit between each other, and how they perform specific functions in real systems. Such a study will make great contribution to discover new laws of chemical dynamics, to explore new control rules of complex chemical processes, to figure out the very roles of chemical reactions in life systems, and to crosslink the scientific study of chemistry, physics and biology. In this mini-review, based on our own work, we mainly give a brief introduction to some frontier topics in the study of nonlinear dynamics in complex chemical systems, namely, nonlinear state-state dynamics, nonlinear chemical dynamics on complex networks, and nonlinear dynamics in mesoscopic chemical reaction systems.

Enhanced corticomuscular coherence by external stochastic noise

“…The phenomenon of enhanced coherence produced by optimal noise has been also described in theoretical models of neurons (Casado, 1997 ; Neiman et al, 1997 ; Pikovsky and Kurths, 1997 ; Lee et al, 1998 ; Wang et al, 2000 ; Zhong and Xin, 2000 ; McMillen and Kopell, 2003 ; Kreuz et al, 2006 ; Torcini et al, 2007 ; Li and Gao, 2008 ; Guo and Li, 2009 ; Jiang and Ma, 2009 ; Franović et al, 2012 ; Gao and Wang, 2012 ; Men et al, 2012 ) and experimentally in physical systems (Lih et al, 1998 ; Postnov et al, 1998 ; Giacomelli et al, 2000 ; Zhong and Xin, 2000 , 2001a , b ; Calvo et al, 2001 ; Zhong et al, 2001 ; Kortlüke et al, 2002 ; Li and Li, 2003 , 2004a , b , c , 2006a , b ; Bahar and Moss, 2004 ; Wang et al, 2010 ; Xin and Hou, 2006 ; Perc, 2007 ; Ermentrout et al, 2008 ; Li et al, 2008 ; Perc et al, 2008 ; Shi and Lang, 2009 ; Shi and Luo, 2010 ). It has been experimentally shown that the SR is related to increased local (within one area) and long-range (between different areas) synchrony.…”